THE SPECTRAL METHOD OF OPTIMAL FILTERING AND EXTRAPOLATION FOR JUMP-DIFFUSION MODELS

Abstract

The article deals with the optimal filtering and extrapolation problems for non-stationary stochastic differential systems with a Poisson component. To find an approximate density of the observed object’s state vector the spectral method based on the representation of robust Duncan-Mortensen-Zakai equation and Kolmogorov-Feller equation solutions in the form of orthogonal series is used.

Keywords

• conditional density
• extrapolation problem
• jump-diffusion
• kolmogorov-feller equation
• filtering problem
• robust duncan-mortensen-zakai equation
• spectral method
• stochastic system