Modeling methods for implicit hereditary stochastic systems

I. N. Sinitsyn

Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119133, Russian Federation

Abstract: The paper is devoted to probabilistic and statistical modeling methods of stochastic processes (StP) in continuous and continuous-discrete implicit hereditary stochastic systems (StS). A survey of methods for probabilistic modeling (MPM) and methods for statistical modeling (MSM) in hereditary StS (HStS) is given. Basic differential implicit HStS are considered. Two practical methods of implicit HStS reduction to differential StS are presented. For smooth and nonsmooth implicit functions, MPM based on the normal approximation method are given for various stages of reduction. Stationary and nonstationary StP are considered. Numerical MSM of various accuracy for reducible differential HStS are considered. Both MPM and MSM for systems described by continuous-discrete implicit equations are given. An illustrative example for scalar integrodifferential with smooth and nonsmooth implicit HStS is presented. Basic conclusions and directions for future investigations are discussed.

Keywords: hereditary stochastic system (HStS), implicit stochastic system, method of probabilistic modeling (MPM), method of statistical modeling (MSM), stochastic process (StP).

Received: 04.03.2024

DOI: 10.14357/08696527240306