Distributions parametrical modeling software for integrodifferential stochastic systems

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 in MATLAB are given.