This article is cited in 5 papers

Probabilistic and statistical modeling methods for implicit 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 article is devoted to probabilistic (analytical) and statistical modeling methods in implicit (continuous, discrete, and continuous-discrete) stochastic systems (StS). A survey in the fields: method of probabilistic modeling (MPM) and method of statistical modeling (MSM) is given. Basic implicit StS reduced to differential, discrete, and continuous-discrete are considered for smooth StS. Main attention is paid to MSM of $h/h^{1/2}$ and $h^2/h^{3/2}$ accuracy. Special attention is paid to the nonsmooth implicit StS. The methods of linear and polynomial regression were implemented. The example is devoted to scalar implicit StS with smooth and nonsmooth functions. Basic conclusions and directions of combined MPM and MSM for StS with inclusions generalizations are given. Canonical expansions of applications to MPM and MSM are suggested.

Keywords: implicit stochastic system, method of probabilistic modeling, method of statistical modeling (MSM), stochastic system with unsolved derivatives (StS USD), strong and weak approximations.

Received: 12.02.2024

DOI: 10.14357/08696527240305