On partially observed jump diffusions I. The filtering equations

2022/05/17 by Germ, Fabian, Gyöngy, István · 1 citation
#60G51 #60H15 #FOS: Mathematics #Optimization and Control (math.OC) #Primary 60G35 #Probability (math.PR) #Secondary 60G57

paper · doi:10.48550/arxiv.2205.08286

Abstract

This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the equation only satisfy appropriate growth conditions. Some results in filtering theory of diffusion processes are extended to jump diffusions and equations for the time evolution of the conditional distribution and the unnormalised conditional distribution of the unobserved process at time t, given the observations until t, are presented.

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