Systems of differential equations modeling non-Markov processes

Irada Dzhalladova and Miroslava Růžičková

Address:
Department of Computer Mathematics and Information Security, Kyiv National Economic University after named V. Hetman, Kyiv 03068, Peremogy 54/1, Ukraine
Department of Analysis, Faculty of Mathematics, University of Białystok, K. Ciołkowskiego 1M, 15-245 Białystok, Poland

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Abstract: The work deals with non-Markov processes and the construction of systems of differential equations with delay that describe the probability vectors of such processes. The generating stochastic operator and properties of stochastic operators are used to construct systems that define non-Markov processes.

AMSclassification: primary 34A37; secondary 34F05, 34K50.

Keywords: non-Markov process, dynamical system with delay, stochastic (generating) operator.

DOI: 10.5817/AM2023-1-21