P. S. Knopov

P. S. Knopov
National Academy of Sciences of Ukraine | ISP · V. M. Glushkov Institute of Cybernetics

Professor

About

188
Publications
2,884
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395
Citations
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January 1962 - January 2016
National Academy of Sciences of Ukraine
Position
  • head of department, professor

Publications

Publications (188)
Article
The paper investigates some stochastic models with discrete and continuous time to solve important problems of predicting the spread of epidemiological diseases in the population. Various factors of epidemic spread and the main parameters influencing the forecast assessment are taken into account. Some test calculations based on the proposed method...
Article
Full-text available
Uncertainty and variability are key challenges for climate change adaptation planning. In the face of uncertainty, decision-making can be addressed in two interdependent stages: make only partial ex ante anticipative actions to keep options open until new information is revealed, and adapt the first-stage decisions with respect to newly acquired in...
Chapter
Many stochastic optimal control problems have analytical solutions up to unknown numerical parameters. We demonstrate this fact with several examples from inventory theory, queuing theory, and risk theory. The paper reviews sufficient conditions for the existence of parametric optimal solutions to such problems in the stationary and nonstationary c...
Conference Paper
Full-text available
Uncertainty and variability of climate changes are key challenges for adaptation planning. In the face of uncertainty, the decision-making can be addressed in two interdependent stages: make only partial ex-ante anticipative actions to keep options open until new information is revealed; and adapt the first-stage decisions with respect to newly acq...
Article
In recent years, a new direction of research has emerged in the theory of stochastic differential equations, namely, stochastic differential equations with a fractional Wiener process. This class of processes makes it possible to describe adequately many real phenomena of a stochastic nature in financial mathematics, hydrology, biology, and many ot...
Chapter
Full-text available
In the presentation we discuss critical issues related to the design of resilient and robust food, water, energy, environmental systems in the presence of interdependent systemic risks. We introduce the notions of systemic risks, security, resilience and robustness in FWEE systems. We emphasize the need for the two-stage preventive-adaptive stochas...
Chapter
Full-text available
The talk illustrates the importance of new type non-smooth stochastic optimization and stochastic quasigradient (SQG) procedures for robust of-line and on-line decisions involving large-scale Machine Learning, Distributed Models Linkage, and robust decision-making problems. Advanced robust statistical analysis and machine learning models based on i...
Preprint
Full-text available
Abstract Many stochastic optimal control problems have analytical solutions up to unknown numerical parameters. We demonstrate this fact with several examples from inventory theory, queuing theory, and risk theory. The paper reviews sufficient conditions for the existence of parametric optimal solutions to such problems in the stationary and non-st...
Article
The work deals with stochastic programming problems for stationary random sequences, stationary processes, homogeneous random fields with discrete and continuous parameters. Trajectories of processes and fields are continuous. Stationary and no stationary observations of processes and fields are considered. The former criterion function is approxim...
Article
P.S.. Knopov, A.S. Korkhin. Statistical analysis of the coronavirus infection dynamics using stepwise switching regression. It is proposed to model of the coronavirus infection dynamics using switching regression, the switching points of which are unknown. The step-by-step process of constructing a regression in time is described. The dynamics of t...
Research Proposal
Full-text available
Проект присвячений рішенню актуальної задачі оцінки епідеміологічної безпеки. Буде створено математичні моделі та методи керування епідемічним процесом для мінімізації негативних медико-біологічних та економічних наслідків епідемій, та визначення ефективних стратегій їх подолання. Результати моделювання дозволять розраховувати динаміку епідемії в у...
Research Proposal
Full-text available
The project is devoted to solving the actual problem of assessing epidemiological safety. In order to minimize the negative medical, biological, and economic impacts of epidemics as well as to determine effective strategies for overcoming them, mathematical models and methods of managing an epidemic process will be created. The simulation results w...
Chapter
Full-text available
Food, Energy, Water (FEW) Nexus for Sustainable Development Goals and Global Intergated Management
Article
Introduction. Due to the spread of COVID-19 in the world, mathematical modeling of epidemiological processes is an important and relevant scientific problem. There are many models describing the dynamics of pandemics, such as the standard SIR model, but most of them are deterministic, while in reality, the processes of infecting and recoveries are...
Preprint
Full-text available
The Covid-19 pandemic poses serious challenges to the world community, requiring adequate methods and means to control it. On the one hand, in the absence of immunity, vaccines and coronavirus drugs in the population, due to the severe consequences of the disease, the epidemic poses a very significant threat to human life and health. On the other h...
Article
Linear regression with switching in continuous time is considered. A method for estimation of switching points and switching regression parameters is described. Examples of its use are given.
Article
The paper considers a stochastic programming problem with the empirical function constructed based on nonstationary observations and continuous time. A random process, stationary in a narrow sense and satisfying the strong mixing condition is investigated in the problem. The conditions under which the empirical estimate is consistent are given and...
Chapter
Full-text available
The single cluster consisting of production leaders of Kyivshchyna is determined on the 2017–2018 data. The cluster covers more than a half of region districts. The region districts do not need raw data generation. The estimates of parameters for Cobb–Douglas production functions are found upon computational data generation. The attainable export o...
Article
Full-text available
Adaptation of the operations research models and methods to planning of the critical infrastructure protection is considered. Adaptation of these models includes taking into account stochastic, informational, and behavioral uncertainty of terrorists. In particular, relevant generalizations of the antagonistic attack–defense game and optimal allocat...
Article
The paper analyzes convergence conditions of the method of observed mean under nonstandard conditions, where dependent observations of random parameters are used and probabilistic optimization functions may be discontinuous indicators. For the case of dependent observations, large deviation type theorems for approximate optimal values and solutions...
Article
Full-text available
The paper analyzes convergence conditions of the sample mean method under nonstandard conditions, where dependent observations of random parameters are used and probabilistic optimization functions may be discontinuous indicators. For the case of dependent observations, large deviation type theorems for approximate optima! values and solutions are...
Chapter
Full-text available
The mathematical problems of complex systems investigation under uncertainties; The main objective of this scientific research is to promote new approaches for sustainable management of the environment through developing new technologies of vulnerability and risk assessment and management for the complex environmental systems for which standard...
Chapter
Full-text available
Розроблено математичні моделі для оцінки ефективності системи природокористування за умов змін клімату та підвищенноє невізначеності Для розрахунку ризиків використовуються методи теорії катастроф. Здійснено оцінку ризиків природокористування на регіональному рівні.
Chapter
Full-text available
W.Wójcik J.Sikora (edit.), Recent Advances in Information Technology; Chapter 6; K Atoyev, P Knopov, V Pepeliaev, P Kisała, R Romaniuk, M Kalimoldayev, The mathematical problems of complex systems investigation under uncertainties (Contents and Abstract); The mathematical problems of complex systems investigation under uncertainties; The main ob...
Chapter
In this paper we consider the large deviation problem for the method of empirical means in stochastic optimization with continuous time observations. For discrete time models this problem was studied in Knopov and Kasitskaya (Cybern Syst Anal 4:52–61, 2004; Cybern Syst Anal 5:40–45, 2010).
Article
Controlled semi-Markov processes for the analysis of a multi-product model of inventory control theory are considered. For this model, under decreasing functions of general costs, the existence conditions for the optimal strategy are found and the existence of optimal (,) s S ?strategy in inventory control is proved.
Poster
The states of Eastern Europe (Ukraine and all the adjacent European states Belarus, Hungary, Moldova, Poland, Romania, Slovakia) have experienced technology and system change in land use since the 1990s. Their total land area exceeds the land area of Mexico or Indonesia, their total gross domestic product (in current US dollars) is between those pr...
Poster
Full-text available
Interdependencies of various risks increase the difficulty of identifying the principal cause of injurious effects and make a system already weakened by stress more susceptible to the effects of additional stressors. In the case of cumulative stressors, a system’s vulnerability possibilities increases nonlinearly. These nonlinearities lead to an in...
Conference Paper
Full-text available
Details and methodology of modeling and robust management of inter-relations between food, water, and energy security in Ukraine is discussed and illustrated with examples. In this study an integrated approach to food-water-energy security management requires the development new approaches, accounting for the specifics of systemic “smart risks” dep...
Article
Full-text available
The paper shows how the mathematical tools of the theory of controlled Markov fields can be applied to model catastrophic risks caused by natural events or terrorist threats. The examples of problem statements of long-term investment in security are given. A survey of solution methods for stochastic optimal control problems is proposed. It is shown...
Article
Full-text available
The paper shows how the mathematical tools of the theory of controlled Markov fields can be applied to model catastrophic risks caused by natural events or terrorist threats. The examples of problem statements of long-term investment in security are given. A survey of solution methods for stochastic optimal control problems is proposed. It is shown...
Chapter
Full-text available
Mathematical models have been created to study the relationship between food, energy and water resources, which allow: 1) to calculate the optimal controls that minimize vulnerability; 2) to study the mechanisms of chaotic regimes that cause instability of complex systems; 3) assess the probability of emergencies of ecological and economic origin....
Article
Full-text available
The mathematical models of sustainable social, economic and environmental development are elaborated. Models allow estimation probability of various emergencies, solving integrated problems of risk management under increased uncertainty caused by global changes.
Chapter
In this chapter we investigate diffusion-type fields and Ito fields on the plane, two-parameter version of the Girsanov theorem, weak and strong solutions of stochastic differential equations on the plane, and the probability measures generated by stochastic fields. The results presented in this chapter are published in [10, 12, 14, 16, 25, 42, 44,...
Chapter
This chapter provides well-known results concerning the properties of two-parametric martingales and stochastic integration on the plane. We begin with the auxiliary chapter, which also contains some facts which are of independent interest. Our standard references for the results below are [20–24, 40, 42, 44, 47, 48, 65, 71].
Chapter
In this chapter we investigate different models of filtration and prediction for stochastic fields generated by some stochastic differential equations. We derive stochastic integro-differentiation equations for an optimal in the mean square sense filter. We also suggest different approaches for finding the best linear estimate for a stochastic fiel...
Chapter
In this chapter we derive the conditions which guarantee the existence of optimal or ε-optimal controls for stochastic systems described by stochastic parabolic differential equation. For random processes similar problems were investigated in [26]. Control problem for some types of processes and fields was discussed also in [18]. Our references for...
Chapter
In this chapter we consider essential problems of stochastic processes with values in a Hilbert space. We present an analogue of the Girsanov theorem for processes of such a type, and some filtration and optimal control problems. Results, exposed in Sects. 5.1 and 5.2, are published in [70], results of Sect. 5.3 are published in [49, 50].
Article
We propose a method to identify the parameters of the “signal plus noise” nonlinear regression model. We investigate the periodogram estimates and prove their strong consistency provided that the noise is a functional of a stationary Gaussian process with long-range dependence and the regression function is almost periodic.
Article
An aggregate mathematical model for country-wide agricultural production is proposed. It allows analyzing various scenarios of crop and livestock production in terms of food security. We developed a mathematical model of agricultural holdings, taking into account weather and economic risks. The model incorporates various factors such as crop insura...
Article
We discuss some aspects of food security in Ukraine concerning the economic availability of food and analyze the current price adjustment procedure for major foods in Ukraine. We develop an alternative procedure, based on an original demand model.
Book
1. Two Parameter Martingales and Their Properties.- 2. Stochastic Differential Equations on the Plane.- 3. Filtration and Prediction Problems for Stochastic Fields.- 4. Control Problem for Diffusion-Type Random Fields.- 5. Stochastic Processes in a Hilbert Space.- References.
Chapter
In stochastic optimization and identification problems (Ermoliev and Wets 1988; Pflug 1996), it is not always possible to find the explicit extremum for the expectation of some random function. One of the methods for solving this problem is the method of empirical means, which consists in approximation of the existing cost function by its empiric e...
Chapter
Consider the regression $${y}_{t} =\tilde{ f}({\mathbf{x}}_{t},{\alpha }^{0}) + {\epsilon }_{ t},\quad t = 1,2,\ldots,$$ (1.1) where y t ∈ℜ 1 is the dependent variable, x t ∈ℜ q is an argument (regressor), α0∈ℜ n is a true regression parameter (unknown), \(\tilde{f}({\mathbf{x}}_{t},\alpha )\) is some (nonlinear) function of α, εt is a noise, and t...
Chapter
In this chapter, we investigate some regression models with unknown coefficients. We assume that the parametric set of unknown parameters is closed and, generally speaking, unbounded. The case of open sets is easier to study, because in most of the cases the asymptotic distribution of estimates is normal. This is not always true when the constraint...
Chapter
In this chapter we investigate statistical properties of the prediction in a regression with constraints. This problem is very complicated, since even in the case of linear regression and linear constraints the estimation of parameters is a nonlinear problem. Especially, the problem of interval prediction, i.e., of finding the confidence interval f...
Chapter
In Sect. 1.2 we consider iterative procedures of estimation of multidimensional nonlinear regression parameters under inequality constraints. Here we investigate asymptotic properties of iterative approximations of estimates, obtained on each iteration. Moreover, we allow the situation when the multidimensional regressor has a trend, for example, i...
Article
For an inventory system with a continuous compact phase state and control set, the existence of the optimal (S, s)-policy is proved and an algorithm for determination of this policy based on stochastic approximation is presented. The cost functions are monotone, continuous, and of a rather general form.
Book
This monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view. Unlike previous publications, this volume analyses the properties of regression with inequality constrains, investigating the flexibility of inequality constrains and their ability to adapt in the pre...
Article
The problems of geological exploration works management in the stage of exploration of an open field are considered. The analysis of the approach to management of the geological exploration process on the basis of monitoring the stabilization of calculated parameters, developed by scientists of the ZapSibNIGNI institute is carried out. This approac...
Chapter
This chapter is devoted to the accuracy of estimation of regression parameters under inequality constraints. In Sects. 4.2 and 4.3 we construct the truncated estimate of the matrix of m.s.e. of the estimate of multi-dimensional regression parameter. In such a construction inactive constraints are not taken into account. Another approach (which take...
Article
Main results obtained by Ukrainian scientists in stochastic optimization are reviewed. Most attention is paid to the results of Yu. M. Ermoliev and his school in quasigradient stochastic programming methods, which are considered classical.
Article
Some problems arising in solving various applied problems of economy, recognition, sociology, biology, and modeling of catastrophes are considered. Such problems can be solved using methods of the theory of Markov random processes with local interaction. General characteristics of such processes and a number of concrete applied problems that can be...
Article
The paper considers a stochastic programming problem with an empirical function constructed based on time-dependent observations. A strictly stationary random sequence that satisfies a strong mixing condition is investigated. The conditions under which an empirical estimate is consistent are given, and large deviations of the estimate are considere...
Article
Full-text available
The information system for complex environmental-technogenic and social-economic risks assessment in the field of housing and communal services is elaborated. It allows: to estimate the deformation of space security under increased uncertainty; to investigate the dynamics of complex risks of disasters as a function of environmental, technogenic, ec...
Article
The paper presents an algorithm to search for the lower bound of the Bayesian estimate of the parameter of exponential distribution in the case where it is known that a priori distribution belongs to the class of all distribution functions with two equal quantiles. This problem arises in sensivity analysis of Bayesian estimates of failure rates to...
Article
Some classes of applied problems from random field theory are discussed and methods to solve them are proposed. Examples from various fields of science and technology are considered. Keywordsrandom fields-useful signal-recognition-random noise-estimate
Article
Sufficient conditions for existence of optimal strategy of control of solution of the stochastic differential equation, which includes additive fractional Brownian process with the Hurst parameter belonging to the interval (0, 1/2).
Article
A stochastic differential equation with respect to fractional Brownian motion is considered. We study the maximum likelihood estimator for the drift coefficient. We assume that the coefficient belongs to a given compact set of functions and prove the strong consistency of the estimator and its asymptotic normality.
Article
A new approach to selecting the Gibbs distribution in models of objects to be recognized is proposed. This approach proposes to determine the lower and upper bounds for probabilities of the object under study. The distance between these bounds may be used as a measure of error in pattern recognition problems.
Article
The asymptotic properties of least-squares estimates of almost periodic signals under random noise are investigated. The consistency and strong consistency of the estimates are proved.
Article
This paper deals with the empirical mean method, which is one of the most well-known methods of solving stochastic programming problems. The authors present their results obtained in recent years and discuss their application to estimation and identification problems.
Article
This paper is devoted to the investigation of a stochastic programming problem with a convex criterion function in the case where the random factor is a stationary ergodic sequence. The problem is approximated by the problem of minimization of an empirical function. It is proved that, under some conditions, the empirical estimate coincides with the...
Article
This paper is devoted to the stochastic optimization problem for a stationary ergodic random sequence satisfying the hypermixing condition. It is assumed that we have a finite number of observed elements in the sequence, and instead of solving the former problem we investigate the empirical function, find its minimum points, and study their asympto...
Article
We consider the procedure for small-sample estimation of reliability parameters. The main shortcomings of the classical methods and the Bayesian approach are analyzed. Models that find robust Bayesian estimates are proposed. The sensitivity of the Bayesian estimates to the choice of the prior distribution functions is investigated using models that...
Article
We introduce the concept of locally acting distributed players into sequential stochastic games with general compact state and action spaces. The state transition function for the system is of local structure as well and this results in Markov properties in space and time for the describing processes. We prove that we can reduce optimality problems...
Article
The authors analyze a stochastic programming problem where the random factor is a stationary ergodic sequence. The problem is approximated by minimizing an empirical function. It is proved that, under some conditions, the probability of large deviations of empirical estimates from the initial problem solution decreases exponentially.
Article
Full-text available
We introduce locally acting distributed decision makers in the theory of semi-Markov decisions for systems for which both the domain and the action space are general and compact. Such decision makers are characterized by making decisions on the basis of the information gathered at their local neighborhood only. The state transient function of the s...
Article
Asymptotic behavior of estimates for unknown parameters of random variables that satisfy a condition of strong hashing is considered. Distribution of functionals of such estimates is normal provided that the true value of the parameter is an interior point.
Article
The paper is a review of some actual problems of risk estimation in identification and control models simulating environmentally dangerous objects, and insurance of catastrophic risks. Main attention is paid to the studies performed at the V.M. Glushkov Institute of Cybernetics.
Article
An inventory model, used to control a one-type product stock with an A-convex cost function is analyzed. The replenishment amount is taken as a control parameter. Strategies that are optimal in the sense of an average expected cost and a total revalued cost with a revaluation coefficient ß are found and examined.
Article
this paper and fundamental investigations on the subject may be found in [1], [2], and with a special emphasis on optimization in [11]
Article
this paper is to develop a general model for describing the interaction of players and coalitions which live on graph structured networks and have to optimize their behavior in sequential stochastic games. This leads immediately to the main questions of the existence of optimal strategies and a value of the games, and to the question whether these...
Article
Trading strategies and utility functions on securities market are considered. It is shown how to find an optimal strategy when the theory of controlled homogeneous Markov chains is used. A corresponding theorem is proved.
Article
Control for a semi-Markovian inventory system is considered. Under general assumptions on system functioning, conditions for existence of an optimal nonrandomized Markovian strategy are found. It is shown that under some additional assumptions on storing conditions for the inventory, the optimal strategy has a threshold (s, S)-frame.
Chapter
In this chapter different cases of parametric regression models are considered.
Chapter
In this chapter some variants of stochastic programming problems are considered. Three cases are investigated: 1) the random factor in the problem is represented by a random element from some metric space, and empirical estimates of the criterion function are made by independent observations of the random element; 2) the random factor is a stationa...
Chapter
In this chapter the nonparametric optimization and estimation models are considered.
Chapter
In this chapter the periodogram estimates of two types are considered. It is proved that the empirical estimates of the parameter converge to its true value with probability 1, and the speed of the convergence is appreciated. Theorems about the strong consistency of the coefficients estimates in the models are proved. The conditions of the asymptot...
Book
Preface. 1. Introduction. 2. Parametric Empirical Methods. 3. Parametric Regression Models. 4. Periodogram Estimates for Random Processes and Fields. 5. Nonparametric Identification Problems. References.
Article
Discrete-time Markovian processes with a multidimensional compact state space are considered, where coordinate processes are locally interacting and change their states synchronously. Conditions are given which guarantee that in the class of local randomized strategies there exist deterministic stationary Markovian strategies which maximize asympto...
Article
The paper considers the problem of optimal input signal estimation for bilinear systems under output measurements. The invertibility notion is introduced for a controlled bilinear system. Lie algebraic invertibility criteria are obtained for bilinear systems in R 2. The necessary conditions are given for invertibility of a nonlinear sensor class, w...
Article
This paper is stimulated by reliability estimation problems for safety systems of Nuclear Power Plants. A new approach for calculating robust Bayes estimators is considered. Upper and lower bounds for Bayes estimates provided that a prior distribution satisfies available prior information, are constructed. The problems of calculating lower and uppe...
Article
Full-text available
this paper was done when the third author visited the Department of Mathematics at Hamburg University. The visit was supported by the Deutsche Forschungsgemeinschaft . 1 simplicity we assume that rejected messages are lost. So by applying such control scheme the overload is handled outside the critical path which the line is considered to be. Consi...
Article
The problem of optimal behavior of insurance company with branches in conditions of operations on the infinite time interval is considered. The moments of insurance payment and their amount are random values. The financial resources replenishment value is taken as the control parameter. Average cost (loss) per time unit is chosen as a criterion. Op...
Article
Models of policy of companies on the market with competing technologies are considered. It is shown that the Gibbs random fields can serve as a convenient formalization for the investigation of such models. In this case the highly developed theory of Markov random fields can be used for analysis and choice of optimal strategies. Bibliography: 14 ti...