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  5. SOLVING ROBUST DUNCAN–MORTENSEN–ZAKAI EQUATION FOR JUMP-DIFFUSION MODELS BY SPECTRAL METHOD

SOLVING ROBUST DUNCAN–MORTENSEN–ZAKAI EQUATION FOR JUMP-DIFFUSION MODELS BY SPECTRAL METHOD

K.A. Rybakov
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In this paper, it is considered the solution of optimal filtering problem for stochastic differential systems with Poisson component. The spectral method is used for the approximate finding of conditional probability density for the system state. This method is based on representation of the solution for robust Duncan–Mortensen–Zakai equation as an expansion over some complete orthonormal system.
Keywords: conditional density, Duncan–Mortensen–Zakai equation, optimal filtering problem, spectral method, stochastic system