On partially observed jump diffusions III
regularity of the filtering density
Fabian Germ (TU Delft - Electrical Engineering, Mathematics and Computer Science)
István Gyöngy (University of Edinburgh)
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Abstract
The filtering equations associated to a partially observed jump diffusion model (Zt)t∈[0,T]=(Xt,Yt)t∈[0,T], driven by Wiener processes and Poisson martingale measures are considered. Building on results from two preceding articles on the filtering equations, the regularity of the conditional density of the signal Xt, given observations (Ys)s∈[0,t], is investigated, when the conditional density of X0 given Y0 exists and belongs to a Sobolev space, and the coefficients satisfy appropriate smoothness and growth conditions.
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