On partially observed jump diffusions I. The filtering equations
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.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.08286
 Bibcode:
 2022arXiv220508286G
 Keywords:

 Mathematics  Probability;
 Mathematics  Optimization and Control;
 Primary 60G35;
 60H15;
 Secondary 60G57;
 60G51
 EPrint:
 27 pages