This article is cited in 2 papers

Statistical modeling of differential stochastic systems with unsolved derivatives

I. N. Sinitsyn<sup>ab

a</sup> Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^b Moscow State Aviation Institute (National Research University), 4 Volokolamskoe Shosse, Moscow 125933, Russian Federation

Abstract: The paper is dedicated to statistical modeling methodological support for differential stochastic systems with unsolved derivatives (StS USD). The basic results are: ($i$) two theorems concerning reduction of stochastic functional-differential equations to stochastic Ito equations; ($ii$) Euler approximation method for stochastic differential equations with Gaussian and Poisson noises; ($iii$) three theorems concerning numerical algorithms of various accuracy for StS USD with smooth nonlinearities; and ($i\nu$) two algorithms for StS USD with nonsmooth nonlinearities. Special attention is paid to methodological aspects of numerical statistical analysis of deterministic and random components in the cases of weak and strong approximation. Directions for further research are given.

Keywords: analytical (probabilistic) modeling, methodological support, statistical modeling, stochastic systems (StS), StS with unsolved derivatives (StS USD).

Received: 18.01.2024

DOI: 10.14357/19922264240302