Filtering and extrapolation in migrational-populational stochastic systems

Approximate quasi-linear filtering and extrapolation methods for migrational-populational stochastic systems (MPStS) are developed. Volterra StS are the special case of MPStS. The MPStS are described by nonlinear differential Ito stochastic equations with additive and parametric noises. Corresponding algorithms are based on the conditionally-optimal linear Pugachev filtering and extrapolation theory. For wide-band noises, simplified approaches for filters synthesis are based on interchange of parametric noises by the additional ones. For narrow-band noise, the methods of Pugachev canonical expansions and generalized canonical expansions corresponding algorithms are proposed. As the test example, three-dimensional differential MPStS with nonlinear stochastic migrational flow with polarized additive and parametric noises is considered. Some special cases are treated. Basic generalizations: (i) nonpolarized and autocorrelated noises in discrete and mixed continuous-discrete MPStS; and (ii) nonlinear filtering and extrapolation in MPStS.