Interpolatonal analytical modeling in complex stochastic systems

Methods and algorithms for interpolational analytical modeling (IAM) of stochastic processes in complex continuous and discrete stochastic systems (StS) which are scalar (or vector StS reducible to scalar) are developed. Several types of continuous and discrete StS are considered. The IAM methods are based on evolutionary equations numerical interpolation solution for one-dimensional characteristic function (c.f.). Special attention is paid to c.f. sensitivity analysis. In basic IAM algorithms, the Kotel'nikov theorem was implemented. Some practical questions concerning interpolational formulae and number of intervals for interpolation are discussed. In the future, IAM for StS with known analytical structure for offline modeling will be based on spline-wavelet methods and for online modeling — on filtration approaches. Special attention should be paid to multidimensional distributions.