Informatics and Applications

2014, Volume 8, Issue 1, pp 2-11


  • I.N. Sinitsyn


Methods and algorithms for statistical and analytical modeling of one- and multidimensional distributions in hereditary stochastic systems (HStS) with Wiener and Poisson noises are considered. Nonlinear stochastic integrodifferential equations are presented. For dying physically realizable hereditary kernels, two ways of approximation (on the basis of linear operator equations and singular kernels) are described. Basic reduction algorithms of HStS to differential StS (DStS) are given. Detailed analysis of various approaches to statistical and analytical modeling of distributions in HStS reducible to DStS is given. These approaches are based: on the direct numerical integration DStS equations and numerical integration of equations for parameters (moments, quasi-moments, etc.) of orthogonal densities expansions. The detailed consideration of the method of statistical linearization (MSL) and of the method of normal approximation (MNA) in reducible HStS to DStS is presented. Numerical stability ofMSL andMNA algorithms is investigated. ForMSL problems, one-step strongmethods and algorithms of numerical integration (of various accuracy) for smooth and nonsmooth right hands ofHStS equations are described. Test examples for the IPI RAS software tool “IDStS” inMATLAB are considered. Special attention is paid to stochastic oscillations of the Duffing oscillator and the relay oscillator in hereditary stochastic media.

[+] References (9)

[+] About this article