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## Publications

Publications (49)

In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function which is defined on bounded domain. A sample input-output cross-correlogram is taken as an estimator of the response function. The input processes are supposed to be zero-mean stationary Gaussian processes that can be represented as th...

In the paper, we consider random variables and stochastic processes from the space Fψ(Ω) and study approximation problems for such processes. The method of series decomposition of stochastic processes from Fψ(Ω) is used to find an approximating process called a model. The rate ofconvergence of the model to the process in the uniform norm is investi...

The paper is devoted to one possible way of the model construction for the stationary Gaussian process with given accuracy and reliability in functional space C ( [ 0 , T ] ) .

The article is devoted to the study of the impulse response function, its estimation and properties, square-Gaussian random variables and processes, the rate of convergence of the unknown impulse response function, testing the hypothesis about the type of impulse response function, building a simulation model. The study showed that the pulse respon...

In recent years, a large number of research of telecommunications traffic have been conducted. It was found that traffic has a number of specific properties that distinguish it from ordinary traffic. Namely: it has the properties of self-similarity, multifractality, long-term dependence and distribution of the amount of load coming from one source....

The investigation of traffic properties of modern networks requires new approaches, the use of adequate types of distributions of traffic components, and measurement errors should be also taken into account. The models of the request flow are approximated by different distributions with “light tails” (Gaussian, Poisson distributions) as well as “he...

In the paper, we consider the problem of simulation of a strictly φ-sub-Gaussian generalized fracti-onal Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are wi...

Today, the theory of random processes and time series prediction is widely used in various fields of science, not only in natural fields. That is why one of the urgent problems is to build a mathematical model of a random process and study its properties. Numerical modeling tasks become especially important due to the powerful capabilities of compu...

The study of the analytical properties of random processes and their functionals, without a doubt, was and remains the relevant topic of the theory of random processes. The first result from which the study of the local properties of random processes began is Kolmogorov’s theorem on sample continuity with probability one. The classic result for Gau...

The problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The...

In the modern rapidly evolving society, the science and the business are facing new needs and challenges constantly. The insurance industry and its mathematical foundation, the actuarial science, are not exceptions. Currently, the greatest challenge that the insurance system has to cope with is the issue of the new international financial standard...

The paper is devoted to the model construction for input stochastic processes of a time-invariant linear system with a real-valued square-integrable impulse response function. The processes are considered as Gaussian stochastic processes with discrete spectrum. The response on the system is supposed to be an output process. We obtain the conditions...

The problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The...

The problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The...

The problem of estimation of unknown response function of a time-invariant continuous linear system is considered. Integral sample input–output cross-correlogram is taken as an estimator of the response function. The inputs are supposed to be zero-mean stationary Gaussian process. A criterion on the shape of impulse response function is given. For...

The integral cross-correlogram estimator of the response function for a linear homogeneous system is considered in this paper. An upper bound for the tail of the distribution of the supremum of the estimation error is found. In the proof, we use some properties of square-Gaussian stochastic processes.

In this chapter, we introduce random Cox processes and describe two algorithms of their simulation with some given accuracy and reliability. The cases are considered when an intensity of random Cox processes are generated by log Gaussian or square Gaussian homogeneous and inhomogeneous processes, or fields are considered. The results of this chapte...

In many applied areas that use the theory of stochastic processes, the problem arises to construct the model of a stochastic process, that is considered as an input process to some system or filter, with respect to the output process. We are interested in the model that approximates a Gaussian stochastic process with respect to the output process w...

The models of Gaussian isotropic random fields on an n-measurable sphere are constructed that approximate these fields with given accuracy and reliability in the space Lp, p ≥ 2.

This chapter offers two approaches to construct the models of Gaussian stationary stochastic processes. These results can be found in the works. The methods of model construction are generalized in the case of random fields. Similar statements are discussed in Tegza’s studies.

A model of a Gaussian stationary process with absolutely continuous spectrum is proposed that simulates the process with given reliability and accuracy in L²(0, T). Under certain restrictions on the covariance function of the process, formulas for computing the parameters of the model are described.

This chapter is devoted to the study of the conditions and rate of convergence of sub-Gaussian random series in some Banach spaces. The results of this chapter are used in other chapters to construct the models of Gaussian random processes that approximate them with specified reliability and accuracy in a certain functional space. Generally, the Ga...

In this chapter, the accuracy and reliability of the models of stationary Gaussian random processes are studied in spaces Lp ([0, T]), p ≥ 1; in Orlicz spaces and in the space of continuous functions C([0, T]). The properties of models of stationary Gaussian processes in a uniform metric, applying the theory of Subφ(Ω) spaces, are investigated. A g...

In this chapter, the results of the first chapter are applied to construct the models of random processes that allow for the representations of either Gaussian or strictly sub-Gaussian series. In the general principles of modeling techniques are considered. Devoted to the models construction of stochastic processes using their Karhunen–Loéve expans...

Simulation has now become an integral part of research and development across many fields of study. Despite the large amounts of literature in the field of simulation and modeling, one recurring problem is the issue of accuracy and confidence level of constructed models. By outlining the new approaches and modern methods of simulation of stochastic...

In this paper a time-invariant continuous linear system with a real-valued impulse response function is considered. A new method for the estimator construction of the impulse response function is proposed. Two criteria on the shape of the impulse response function are given. In this paper a time-invariantcontinuous linear system with a real-valued...

An exact asymptotic value of the logarithm for a counting
process in the max-scheme is obtained.

We establish an expansion for a class of second-order stochastic processes in series with uncorrelated summands. Results concerning uniform convergence of such series are proved. A representation for random variables present in these series is obtained under certain restrictions. Simulation of Gaussian processes with given accuracy and reliability...

A paper is devoted to new expansions of random processes in the form of series. In particular case the expansions in series of stationary stochastic processes with absolutely continuous spectral function and the expansions with respect to some functions which generate wavelet basis are obtained. These results are used for model construction of stoc...

Stochastic processes of the space Subφ(Ω) are considered in the paper. We prove upper bounds for large deviation probabilities and construct models of stochastic processes in the space C[0, 1] with a given accuracy and reliability. Strongly sub-Gaussian processes are also considered as a particular case.

Separable stochastic processes with discrete spectrum from the space Sub φ (Ω) are considered. For these processes the approximating models with a given reliability and accuracy are constructed in the Banach space C[0;1].

In this paper the Gaussian stochastic processes, represented in the form of series, are considered. The approximating models of the Gaussian processes with given reliability and accuracy in Banach space C

In the paper the simulation of Gaussian stochastic processes is considered. For this purpose the estimation for distribution of supremum of square-Gaussian processes is found. This result is used for model construction of Gaussian stochastic process, taking into account the derivative of the process, with given reliability and accuracy in Banach sp...