Systems and Means of Informatics
2014, Volume 24, Issue 1, pp 4-45
DISTRIBUTIONS PARAMETRICAL MODELING SOFTWARE
FOR INTEGRODIFFERENTIAL STOCHASTIC SYSTEMS
- I. N. Sinitsyn
- I. V. Sergeev
- V. I. Sinitsyn
- E. R. Korepanov
- V. V. Belousov
Abstract
Methods and algorithms for analytical and statistical modeling of
one- and multidimensional distributions in integrodifferential stochastic system
(IDStS) are considered. Nonlinear Ito equations for IDStS with Wiener and
Poisson noises are presented. For dying physically realizable integral kernels, two
methods of IDStS reduction to differential stochastic system (DStS) are given for
dying physical realizable integral kernels (based on linear operator equations and
singular kernels). Different approaches for numerical analytical and statistical
modeling for IDStS reducible to DStS are discussed. Two numerical methods
for practical applications are presented: normal approximation method (for
nonadditive noises) and statistical linearization method (for additive noises).
Special attention is paid to pure direct numerical methods for continuos and
discontinuos right hands of equations. Test examples and results of computer
experiments carried out by the \IDStS" software tool inMATLAB are given.
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[+] About this article
Title
DISTRIBUTIONS PARAMETRICAL MODELING SOFTWARE
FOR INTEGRODIFFERENTIAL STOCHASTIC SYSTEMS
Journal
Systems and Means of Informatics
Volume 24, Issue 1, pp 4-45
Cover Date
2013-11-30
DOI
10.14357/08696527140101
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
analytical modeling; differential stochastic system; generalized Ito
formula; hereditary system; integrodifferential stochastic system; Ito stochastic
differential equation; singular kernels; software; statistical modeling
Authors
I.N. Sinitsyn  , I. V. Sergeev , V. I. Sinitsyn , E. R. Korepanov , and V. V. Belousov
Author Affiliations
Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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