Informatics and Applications
2014, Volume 8, Issue 2, pp 2-14ANALYTICAL MODELING OF DISTRIBUTIONS WITH INVARIANT MEASURE IN NON-GAUSSIAN DIFFERENTIAL AND REDUCABLE TO DIFFERENTIAL HEREDITARY STOCHASTIC SYSTEMS
- I.N. Sinitsyn
Abstract
Exact and approximate methods and algorithms of one- and multidimensional distributions with invariant measure for analytical modeling in differential non-Gaussian (with Wiener and Poisson noises) stochastic systems (StS) and hereditary StS (HStS) reducible to differential are presented. Four theorems giving exact methods of analysis modeling in differential StS (DStS) of general type are proved. Approximate methods based on distributions parametrization in DStS are disscused. Special attention is paid to the methods of normal approximation (MNA) and statistical linearization (MSL) for one- and dimensional distributions in DStS. Stability conditions are presented. three theorems giving exact and approximate analytical modeling in HStS resucible to DStS with asymptotically dying kernels are given. Some equavalency applications of DStS and HStS are considered. Test examples for software tools "ID StS" are given.[+] References (25)
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[+] About this article
Title
ANALYTICAL MODELING OF DISTRIBUTIONS WITH INVARIANT MEASURE IN NON-GAUSSIAN DIFFERENTIAL AND REDUCABLE TO DIFFERENTIAL HEREDITARY STOCHASTIC SYSTEMSJournal
Informatics and Applications2014, Volume 8, Issue 2, pp 2-14
Cover Date
2014-03-31DOI
10.14357/19922264140201Print ISSN
1992-2264Publisher
Institute of Informatics Problems, Russian Academy of SciencesAdditional Links
Key words
analytical modeling; differential stochastic system; distribution with invariant measure; Gaussian (normal) stochastic system; hereditary kernel; hereditary stochastic system; hereditary system reducible to differential; Ito stochastic differential equation; method of statistical linearization; non-Gaussian (with Wiener and Poisson noises) stochastic system; normal approximation method; singular kernel; software tools "ID StS"Authors
I.N. Sinitsyn
Author Affiliations
Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian
Federation