Analytical Modeling and Estimation of Normal Processes Defined By Stochastic Differential Equations with Unsolved Derivatives
Published on: 2021-02-05
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KeywordsMethod of analytical modeling (MAM); Multiplicated noise; Pugachev estimators (filters, extrapolators etc); Regression model (deterministic and stochastic); Stochastic differential equations with unsolved derivatives (SDE USD)
Approximate methods of analytical modeling (MAM) of the wide band stochastic processes (StP) in stochastic differential equations with unsolved derivatives (SDE) USD) based on normal approximate method (NAM), orthogonal expansions method and quasimoment methods are developed in [1, 2]. For stochastic integrodifferential equations with unsolved derivatives (SIDE USD) reducible to SDE corresponding Eqs for MAM are given in [3, 4]. In [3,4] problems of mean square (m.s.) synthesis of normal (Gaussian) estimators (filters, extrapolators, etc) where firstly stated and solved for filtering. Results presented in [1-4] are valid only for sooth (in m.s. sense) functions in SDE USD.
Let us generalize [1-3] results for unsmooth functions in SDE USD for normal filtering and extrapolation. Section 2 is dedicated to SDE USD. In Section 3 deterministic and stochastic regression models for SDE USD are discussed. Section 4 and 5 are devoted to normal m.s. filtering and extrapolation. Examples are given in Section 6. In Section 7 applications to SDE USD with multiplicated Gaussian noises are given. Conclusion contains some remarks concerning future generalizations.