Franco Pellerey

Franco Pellerey
Politecnico di Torino | polito · DISMA - Department of Mathematical Sciences

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94
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November 1998 - present
Politecnico di Torino
Position
  • Full Professor - Probability and Statistical Mathematics

Publications

Publications (94)
Chapter
Given a multivariate random vector, Efron’s marginal monotonicity (EMM) refers to the stochastic monotonicity of the variables given the value of their sum. Recently, based on the notion of total positivity of the joint density of the vector, Pellerey and Navarro (2021) obtained sufficient conditions for EMM when the monotonicity is in terms of the...
Chapter
Let X be a random variable with distribution function F and let \(\mathcal {F}_X\) be the family of proportional reversed hazard rate distribution functions associated to F. Given the random vector (X, Y) with copula C and respective marginal distribution functions F and \(G\in \mathcal {F}_X,\) we obtain sufficient conditions for the existence of...
Article
For a given pair of random lifetimes whose dependence is described by a time-transformed exponential model, we provide analytical expressions for the distribution of their sum. These expressions are obtained by using a representation of the joint distribution in terms of bivariate distortions, which is an alternative approach to the classical copul...
Article
Full-text available
Closure of aging classes with respect to sums is a relevant topic in different areas of applied probability. In the case of independent random variables (i.e., for convolutions) this preservation property has been proved in the literature for a number of classes such as the increasing in likelihood ratio (ILR) and the increasing failure rate (IFR)...
Article
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Given a finite set of independent random variables, assume one can observe their sum, and denote with s its value. Efron in 1965, and Lehmann in 1966, described conditions on the involved variables such that each of them stochastically increases in the value s, i.e., such that the expected value of any non-decreasing function of the variable increa...
Article
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New weak notions of positive dependence between the components X and Y of a random pair (X,Y) have been considered in recent papers that deal with the effects of dependence on conditional residual lifetimes and conditional inactivity times. The purpose of this paper is to provide a structured framework for the definition and description of these no...
Article
Full-text available
Several studies have shown so far that poor acoustics inside classrooms negatively affects the teaching and learning processes, especially at the lowest grades of education. However, the extent to which noise exposure or excessive reverberation affect well-being of children at school in their early childhood is still unanswered, as well as their aw...
Article
Consider a vector (X,Y) that describes the failure times of two non-independent components of a system. Assuming that the first component has survived up to a given time t>0, i.e., assuming X>t, one can define the corresponding residual lifetime under different assumptions on the failure of the second component, having lifetime Y. In particular, on...
Article
Full-text available
Among Mixed Poisson processes, counting processes having geometrically distributed increments can be obtained when the mixing random intensity is exponentially distributed. Dealing with shock models and compound counting models whose shocks and claims occur according to such counting processes, we provide various comparison results and aging proper...
Article
The paper presents the results of a research project carried out by a team of researchers from the Inter-university Department of Regional and Urban Studies and Planning of the Politecnico di Torino and financed by the Autonomous Province of Trento. The Territorial Integrated Evaluation (TIE) methodology was applied in Trentino in order to analyse...
Article
A set of logistic mathematical models to estimate the daylight amount and the energy demand for lighting of a room is presented. The models were built upon a database of results obtained for a sample room through Daysim simulations: features such as site, orientation, external obstructing angle, window size, glazing visible transmittance and room d...
Article
Full-text available
Recent literature reports that a large percentage of teachers complain that teaching has an adverse effect on their voice status. Thus, more needs to be done to study their vocal behavior. The objective of this longitudinal study was twofold: to determine changes in the voice use of teachers over a school year, and to study the relationships betwee...
Article
The accurate prediction of windblown sand drift events approaching human infrastructures and activities is fundamental in arid lands. In both scientific literature and technical practice sand drift estimation is carried out in mean terms. Typically, sand drift net direction and intensity are assessed by means of the resultant drift potential. Howev...
Article
Coherent systems, i.e., multicomponent systems where every component monotonically affects the working state or failure of the whole system, are among the main objects of study in reliability analysis. Consider a coherent system with possibly dependent components having lifetime T, and assume we know that it failed before a given time \(t>0\). Its...
Conference Paper
Full-text available
This longitudinal work explores the relationships between three analyses used for assessing teachers’ voice use: the voice monitoring during lessons that describes the teachers’ Vocal Behavior (VB), the perceptual assessment of voice by speech-language pathologists and the estimation of objective parameters from vocalizations to define teachers’ Vo...
Article
The reliable prediction in probabilistic terms of the consequences of aeolian events related to sand transport phenomena is a key element for human activities in arid regions. Threshold shear velocity generating sand lifting is a key component of such a prediction. It suffers from the effect of uncertainties of different origin, such as those relat...
Conference Paper
Full-text available
The objective of this longitudinal study is twofold: to determine changes in the voice use of teachers along a school year and to study the relationships between voice and classroom acoustics parameters, which account for the background noise level during the teaching hours too. Thirty-one teachers from two secondary schools in Torino (Italy) were...
Article
In this paper, we define and study a new notion for the comparison of the hazard rates of two random variables taking into account their mutual dependence. Properties, applications and the comparison for a data set are given.
Article
A new property defined on the class of symmetric copulas is introduced and studied along this note. It is shown here that such a property can define a family of bivariate distribution functions satisfying all the characteristics listed in Kimeldorf and Sampson (1989) to be considered as a positive dependence notion. Applications, relationships with...
Article
Full-text available
A weak version of the joint hazard rate order, useful to stochastically compare not independent random variables, has been recently defined and studied in [4]. In the present paper, further results on this order are proved and discussed. In particular, some statements dealing with the relationships between the jointweak hazard rate order and other...
Article
An innovative integrated self-learning health monitoring system has been developed and implemented on a fleet of helicopters in actual service. This system improves significantly the efficiency of a previous accelerometric vibrational monitoring tool by means of multivariate third level processing of the accelerometric features. The paper describes...
Article
The frailty approach is commonly used in reliability theory and survival analysis to model the dependence between lifetimes of individuals or components subject to common risk factors; according to this model the frailty (an unobservable random vector that describes environmental conditions) acts simultaneously on the hazard functions of the lifeti...
Article
Recently some well-known univariate aging classes of lifetime distributions have been characterized by means of properties of their quantile functions and excess-wealth functions. The generalization of the univariate aging notions to the multivariate case involve, among other factors, appropriate definitions of multivariate quantiles or regression...
Article
Consider a general coherent system with independent or dependent components, and assume that the components are randomly chosen from two different stocks, with the components of the first stock having better reliability than the others. Then here we provide sufficient conditions on the component’s lifetimes and on the random numbers of components c...
Chapter
In many applicative fields, the behavior of a process \(\mathbf {Z}\) is assumed to be subjected to an underlying process \(\varTheta \) that describes evolutions of environmental conditions. A common way to define the environmental process is by letting the marginal values of \(\varTheta \) subjected to specific environmental factors (constant alo...
Article
In this note we consider a vector (X1;X2) of lifetimes whose dependence is described by an Archimedean copula, and we provide conditions useful to describe the relationships between ageing properties of X1 and X2 and ageing properties of their minimum. Examples are also provided. © 2014, Hacettepe Journal of Mathematics and Statistics. All rights r...
Article
The paper presents a set of logistic mathematical models to quickly estimate, since the earliest design stages, the electric lighting energy demand for a generic room with different architectural features (site, orientation, external obstructing angle, window size, glazing visible transmittance and room depth), lighting system characteristics or us...
Article
In order to take into account any possible dependence between alternatives in optimization problems, bivariate characterizations of some well-know univariate stochastic orders have been defined and studied by Shanthikumar and Yao (Adv Appl Probab 23:642–659, 1991). These characterizations gave rise to new stochastic comparisons, commonly called joi...
Article
The implementation into service of accelerometric health monitoring systems of mechanical power drives on helicopters has shown that the generation of false failure alarms is a critical issue. The paper presents a combined application of several multivariate statistical techniques and shows how a monitoring method which integrates these tools can b...
Article
Full-text available
Consider random vectors formed by a finite number of independent groups of independent and identically distributed random variables, where those of the last group are stochastically smaller than those of the other groups. Conditions are given such that certain functions, defined as suitable means of supermodular functions of the random variables of...
Article
Bivariate aging notions for a vector X of lifetimes based on stochastic comparisons between X and X t, where X t is the multivariate residual lifetime after time t > 0, have been studied in Pellerey (2008) under the assumption that the dependence structure in X is described by an Archimedean survival copula. Similar stochastic comparisons between X...
Chapter
Consider an n–component coherent system having random lifetime \(T_{\boldsymbol{X}}\), where \(\boldsymbol{X} = (X_{1},\ldots,X_{n})\) is the vector of the non-independent components’ lifetimes. Stochastic comparisons of the residual life of \(T_{\boldsymbol{X}}\) at a fixed time t ≥ 0, conditioned on \(\{T_{\boldsymbol{X}} > t\}\) or on \(\{X_{i}...
Article
In this note we compare bivariate additive models with respect to their Pearson correlation coefficients, Kendall’s ττ concordance coefficients, and Blomqvist ββ medial correlation coefficients. The conditions that enable the comparisons involve variability stochastic orders such as the dispersive and the peakedness orders. Specifically we show tha...
Article
Customer satisfaction data collected by a large cellular phone service provider are to be used to evaluate and improve the quality of their service. For this purpose, we propose a Bayesian treatment of a joint-response chain graph relating partial assessments of specific aspects of quality to an overall assessment of the service quality. The result...
Article
In this paper we introduce a new multivariate stochastic order that compares random vectors in a direction which is determined by a unit vector, generalizing previous upper and lower orthant order. The main properties of this new order, together with its relationships with other multivariate stochastic orders, are investigated and, we present some...
Article
We consider the problem of stochastic comparison of general Garch-like processes, for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the Garch process itself, and discuss their interpretations. We focus on the convex order and show that in the ca...
Article
Full-text available
This work presents an approach used to assess the quality of soundscape in urban spaces. It consists in analyzing and correlating psychometric tools that measure the perception of environmental quality and in correlating subjective acoustic data with objective investigation of acoustic parameters. Survey has considered selected key-spaces of two di...
Article
Since multivariate lifetime data frequently occur in applications, various properties of multivariate distributions have been previously considered to model and describe the main concepts of aging commonly considered in the univariate setting. The generalization of univariate aging notions to the multivariate case involves, among other factors, app...
Article
A class of generalized bivariate Marshall–Olkin distributions, which includes as special cases the Marshall–Olkin bivariate exponential distribution and the Marshall–Olkin type distribution due to Muliere and Scarsini (1987) [19] are examined in this paper. Stochastic comparison results are derived, and bivariate aging properties, together with pro...
Article
In this paper, some new properties of the upper-corrected orthant of a random vector are proved. The univariate right-spread or excess wealth function, introduced by Fernández-Ponce et al. (1996), is extended to multivariate random vectors, and some properties of this multivariate function are studied. Later, this function was used to define the ex...
Article
Consider a series or parallel system of independent components and assume that the components are randomly chosen from two different batches, with the components of the first batch being more reliable than those of the second. In this note it is shown that the reliability of the system increases, in usual stochastic order sense, as the random numbe...
Article
We discuss suitable conditions such that the lifetime of a series or of a parallel system formed by two components having nonindependent lifetimes may be stochastically improved by replacing the lifetimes of each of the components by an independent mixture of the individual components' lifetimes. We also characterize the classes of bivariate distri...
Article
Full-text available
Let X = (X, Y) be a pair of lifetimes whose dependence structure is described by an Archimedean survival copula, and let X t = [(X − t, Y − t) | X > t, Y > t] denotes the corresponding pair of residual lifetimes after time t ≥ 0. Multivariate aging notions, defined by means of stochastic comparisons between X and X t , with t ≥ 0, were studied in P...
Article
Consider two random vectors X1 and X2 whose distributions are defined according to the multivariate frailty approach, and let Xk,t=[Xk−t|Xk>t], k=1,2, be the corresponding vectors of residual lifetimes at . Conditions for multivariate stochastic comparisons of random vectors described by the frailty approach have been recently presented in Misra et...
Article
Different sufficient conditions for stochastic comparisons between random vectors have been described in the literature. In particular, conditions for the comparison of random vectors having the same copula, i.e., the same dependence structure, may be found in Müller and Scarsini (2001). Here we provide conditions for the comparison, in the usual s...
Article
Full-text available
Let X = (X, Y ) be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let X t = ((X ¡ t, Y ¡ t)jX > t, Y > t) denotes the corresponding pair of residual lifetimes after time t, with t ‚ 0. This note deals with stochastic comparisons between X and X t: we provide sufficient conditions for...
Article
Recently, Belzunce, Ortega, Pellerey, and Ruiz [3] have obtained stochastic comparisons in increasing componentwise convex order sense for vectors of random sums when the summands and number of summands depend on a common random environment, which prove how the dependence among the random environmental parameters influences the variability of vecto...
Article
Full-text available
A subjective survey on perceived environmental quality has been carried out on 51 secondary-school classrooms, some of which have been acoustically renovated, and acoustical measurements were carried out in eight of the 51 classrooms, these eight being representative of the different types of classrooms that are the subject of the survey. A questio...
Article
A bisexual Galton-Watson branching process is a two-type branching model, in which matings in one generation give rise to random numbers of both males and females in the next. The mating function describes how many mating units are formed from given numbers of males and females. In this paper we consider the case that the distributions of the rando...
Article
In this note we consider branching processes whose behavior depends on a dynamic random environment, in the sense that we assume that the offspring distributions of individuals are parametrized, over time, by the realizations of a process describing the environmental evolution. We study how the variability in time of the environment modifies the va...
Article
In this note we consider branching processes whose behavior depends on a dynamic random environment, in the sense that we assume that the offspring distributions of individuals are parametrized, over time, by the realizations of a process describing the environmental evolution. We study how the variability in time of the environment modifies the va...
Article
Different aggregate preference orders based on rankings and top choices have been defined in the literature to describe preferences among items in a fixed set of alternatives. A useful tool in this framework is constituted by random utility models, where the utility of each alternative, or object, is represented by a random variable, indexed by the...
Article
Full-text available
This paper examines the market bounds in order to describe the evolution of investor's op- timal choices. Thus, first we describe the distributions of market bounds when limited short sales are allowed. Then, we introduce a linear approximation model that describes the investors' optimal choices as a function of the upper market bound. Finally, we...
Article
Dependencies among random numbers of summands in random sums or among summands have been widely studied in recent literature, and several applications have been developed in actuarial sciences and reliability, where dependencies among risks or lifetimes are quite usual in common problems. In this note we derive stochastic comparisons for random sum...
Article
In this note we provide new results of interest in the portfolio choice problem when the risky opportunities are correlated: for a general vector (X 1, X 2,..., X n ) of risky opportunities we give new conditions for stochastic comparison among different portfolios choices and new necessary and sufficient conditions to characterize the portfolio wh...
Article
The purpose of this article is to study several preservation properties of the mean inactivity time order under the reliability operations of convolution, mixture, and shock models. In that context, the increasing mean inactivity time class of lifetime distributions is characterized by means of right spread order and increasing convex order. S...
Article
In this paper we define two stochastic processes that are smaller and greater in usual stochastic order than the Sparre Andersen process. We derive, as a consequence, upper and lower bounds of its marginal distributions, and of the distributions of its first passage times above fixed thresholds. We also present a generalization of these stochastic...
Article
The Laplace transform of residual lives order has been recently defined and studied in the literature to compare random lifetimes. Here, we prove that such stochastic order is equivalent to the well-known hazard rate order. As consequences, we get new characterizations of the hazard rate order and increasing in failure rate (IFR) aging notion, in t...
Article
The paper by M.I. Hendi et al. (see J. Appl. Probability, vol.30, p.975-8) proves that the family of new better than used in convex order (NBUC) distributions is closed under the formation of parallel systems with i.i.d components. This paper proves, through a simple argument based on stochastic orders, that this property also holds for s-independe...
Article
We show that for every fixed time t ≥ 0 the marginal of the classical integrated telegrapher's process increases in the convex order if the rate of the undelying Poisson process decreases.
Article
Consider m counting processes Γi,i=1,2,…,m, and a random vector of positive integers M=(M1,M2,…,Mm). Denote by Xij the jth interpoint interval in the process Γi,i=1,2,…,m,j=1,2,…, and define Zi=∑j=1MiXij,i=1,2,…,m. It is assumed that M is independent of the Γi's, however, the processes Γi's are not necessarily mutually independent. In this paper we...
Article
Ebrahimi (2001) proposes an interesting model for assessing a system's reliability, expressing the failure time of the system in terms of a deterioration process and covariates. He also provides illustrative examples and gives some properties of the model. In this note, we give conditions for negative ageing of the system's lifetime, and we correct...
Article
Ebrahimi (2001) proposes an interesting model for assessing a system's reliability, expressing the failure time of the system in terms of a deterioration process and covariates. He also provides illustrative examples and gives some properties of the model. In this note, we give conditions for negative ageing of the system's lifetime, and we correct...
Article
The geometric telegrapher's process is proposed as a model to describe the dynamics of the price of risky assets. When the underlying random inter-times have Erlang distribution we express the probability law of such process in terms of a suitable two-index pseudo-Bessel function. Stochastic comparisons of two geometric telegrapher's processes base...
Article
The problem of the preservation of non-parametric life distributions classes under addition of life lengths has been extensively studied in literature. In literature, however, independence among the random life lengths is often assumed. Here we show that for the HNBUE life distributions class (and for some other larger classes) this preservation pr...
Article
Full-text available
In this article, we identify conditions under which the epoch times and the interepoch intervals of a nonhomogeneous Poisson process have logconcave densities. The results are extended to relevation counting processes. We also study discrete-time counting processes and find conditions under which the epoch times and the interepoch intervals of thes...
Article
Consider two devices subjected to shocks arriving according to two identically defined counting processes. Let N1 and N2 be the random numbers of shocks until failure of the two devices, respectively, and let T1 and T2 be their random lifetimes. Conditions such that stochastic orders between N1 and N2 are preserved by T1 and T2 have been investigat...
Article
LetX andY be two random variables with finite expectationsE X andE Y, respectively. ThenX is said to be smaller thanY in the dilation order ifE[ϕ(X-E X)]≤E[ϕ(Y-E Y)] for any convex functionϕ for which the expectations exist. In this paper we obtain a new characterization of the dilation order. This characterization enables us to give new interpreta...
Article
For a component operating in random environment, whose hazard rate is assumed to be the realization of a suitable increasing stochastic process, conditions are found such that its lifetime is increasing in likelihood ratio (ILR). For the lifetimes of two components of the same kind some comparisons based on partial stochastic orders are presented....
Article
A new necessary condition for higher order stochastic dominances based on the sequences of the iterated equilibrium distributions of the risks is presented. As application we present alternative simpler proofs of some known moment inequalities related to these dominances.
Article
Some moment inequalities are knwon to be valid for non-parametric lifetime distribution classes. Here we consider one set of these inequalities, which hold for random variables that are DMRL (decreasing in mean residual life). We prove that such inequalities are satisfied by variables which are sums of DMRL random variables too, though these sums a...
Article
Some moment inequalities are known to be valid for non-parametric lifetime distribution classes. Here we consider one set of these inequalities, which hold for random variables that are DMRL (decreasing in mean residual life). We prove that such inequalities are satisfied by variables which are sums of DMRL random variables too, though these sums a...
Article
The purpose of this note is to show a new characterization of the IFR and DFR aging notions by means of the dispersive order. Our result extends results of L. Mailhot [C. R. Acad. Sci., Paris, Sér. I 304, 499-501 (1987; Zbl 0617.60015)] and of F. Belzunce, J. Candel and J. M. Ruiz [Stat. Probab. Lett. 28, No. 4, 321-327 (1996; Zbl 0854.62011)]. Our...
Article
One purpose of this paper is to study the relationship of the dilation order ([less-than-or-equals, slant]dil) to two other stochastic orders: the mean residual life order ([less-than-or-equals, slant]mrl) and the increasing convex order ([less-than-or-equals, slant]icx). Regarding these orders, it is already known that X [less-than-or-equals, slan...
Article
The preservation under convolutions and mixing of the increasing convex comparison of risks is considered, and new related results are proved. Some applications of these results in actuarial context are shown. Also, similar properties are shown to be satisfied by the convex and the Laplace comparisons of risks.
Article
Many stochastic processes considered in applied probability models, and, in particular, in reliability theory, are processes of the following form: Shocks occur according to some point process, and each shock causes the process to have a random jump. Between shocks the process increases or decreases in some deterministic fashion. In this paper we s...
Article
A new partial ordering among life distributions in terms of their uncertainties is introduced. Our measure of uncertainty is Shannon information applied to the residual lifetime. The relationship between this ordering and various existing orderings of life distributions are discussed. Various properties of our proposed concept are examined. Based o...
Article
A new partial ordering among life distributions in terms of their uncertainties is introduced. Our measure of uncertainty is Shannon information applied to the residual lifetime. The relationship between this ordering and various existing orderings of life distributions are discussed. Various properties of our proposed concept are examined. Based o...
Article
Partial stochastic orderings of risks have received considerable attention in recent literature on actuarial theory and its applications. Here the Mean Remaining Life ordering and the Harmonic Average Mean Remaining Life ordering are considered, and their stability under deterministic and random summation is studied.
Article
Two devices are subjected to shocks arriving according to a general counting process. Let M1 and M2 be the random number of shocks that cause the failure of the first and the second device, respectively. We find conditions on the counting process such that the mean residual life ordering, the increasing convex ordering and the expectation ordering...
Article
Recently defined classes of life distributions are considered, and some relationships among them are proposed. The life distribution H of a device subject to shocks occurring randomly according to a Poisson process is also considered, and sufficient conditions for H to belong to these classes are discussed.
Article
Recently defined classes of life distributions are considered, and some relationships among them are proposed. The life distribution H of a device subject to shocks occurring randomly according to a Poisson process is also considered, and sufficient conditions for H to belong to these classes are discussed.
Article
Suppose that a device is subjected to shocks governed by a counting process N={N(t),t≥0}. The probability that the device survives beyond time t is then H ¯(t)=∑ k=0 ∞ Q ¯ k ℙ[N(t)=k], where Q ¯ k is the probability of surviving k shocks. It is known that H is NBU if the interarrivals U k , k∈ℕ + , are independent and NBU, and Q ¯ k+j ≤Q ¯ k ·Q ¯ j...
Article
Suppose that a device is subjected to shocks governed by a counting process N = {N(t), t ≧0}. The probability that the device survives beyond time t is then H̄(t)=Σk=0∞Q̄ℙ[N(t)=k], where Q̄k is the probability of surviving k shocks. It is known that H is NBU if the interarrivals Uk , ∊ ℕ+, are independent and NBU, and Q̄ k+j ≦ Q̄k · Q̄j holds whene...
Article
Two devices are subjected to common shocks arriving according to two identical counting processes. Let P̄k and Q̄k denote the probability of surviving k shocks for the first and the second device, respectively. We find conditions on the discrete distributions {P̄k, k=0,1,⋯ } and {Q̄k, k=0,1,⋯ } in order to obtain the failure rate order (FR), the li...
Article
Two devices are subjected to common shocks arriving according to two identical counting processes. Let and denote the probability of surviving k shocks for the first and the second device, respectively. We find conditions on the discrete distributions and in order to obtain the failure rate order (FR), the likelihood ratio order (LR) and the mean r...
Article
New concepts of partial stochastic orderings are introduced, and the relations among them and the classical partial orderings are shown. Relevance of these partial orderings in aging properties classification is discussed, and new classes of life distributions, based on them, are proposed. An application to stochastic comparison between Poisson sho...
Article
Let [NA(t), t≥0] and [NB(t), t≥0] be two counting processes with independent interarrivals Ai and Bi, respectively, i + ≡ [1,2,… ], and let [Xi, i +] and [Yi, i +] be two sequences of independent non-negative random variables. Consider the two compound processes [U(t), t ≥ 0] and [V(t), t ≥ 0] defined as U(t) = Xi, t ≥ 0, and V(t) = Yi, t ≥ 0. Then...
Article
Full-text available
Consider two vectors X1 and X2 of random lifetimes whose distributions are dened via the frailty approach, and let Xk;t = (Xk tj Xk > t), k = 1; 2, be the corresponding vectors of residual lifetimes at t = (t1;:::;tn);ti 2 R+;i = 1;:::;n. Here we describe sucient conditions for the stochastic comparison X1;t st X2;t for every vector t of non-negati...

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