# On nonlinear filtering of jump diffusions

#### Speaker: Prof. Istvan Gyongy (University of Edinburgh)

Partially observed jump diffusions $Z_t=(X_t,Y_t)$ on a time interval $[0,T]$ are considered. The classic problem of describing the mean square estimate for the unobserved component’ $X_t$ from past observations' $Y_s$, $s\leq t$ is discussed. Stochastic integro-differential equations for the conditional distribution $\mu_t(dx)$ of $X_t$, given the past observations, are shown, and recent results on the existence of the density $\mu_t(dx)/dx$ and its analytical properties are presented.

The talk is based on joint work with Sizhou Wu and Fabian Germ.

If you are interested to join this talk, please contact Dr Miryana Grigorova at m.r.grigorova@leeds.ac.uk for the Zoom details.

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