APPROXIMATE FILTER FOR JUMP-DIFFUSION MODELS

Abstract

A new approach to the optimal filtering problem for jump-diffusion models is considered in this paper. This approach is based on the statistical modeling method (Monte Carlo method). It is assumed that the observation object and measurement system are described by Itô stochastic differential equations, the observation object equation has compound Poisson component, which allows simulating impulse noises and perturbations for control system. These results have shown that the optimal filtering problem for jump-diffusion models can be solved as an analysis problem for the special stochastic system with jumps, branching and terminating trajectories.

Keywords

• branching processes
• conditional density
• duncan-mortensen-zakai equation
• jump-diffusion
• kushner-stratonovich equation
• monte carlo method
• optimal filtering problem
• stochastic system