### Kalman-Bucy filter and SPDEs with growing lower-order coefficients in W1p spaces without weights.

Krylov, N *(University of Minnesota)*

Monday 14 June 2010, 09:50-10:40

Seminar Room 1, Newton Institute

#### Abstract

We consider divergence form uniformly parabolic SPDEs with VMO bounded leading coefficients, bounded coefficients in the stochastic part, and possibly growing lower-order coefficients in the deterministic part. We look for solutions which are summable to the p-th power, p=2, with respect to the usual Lebesgue measure along with their first-order derivatives with respect to the spatial variable. Our methods allow us to include Zakai's equation for the Kalman-Bucy filter into the general filtering theory.

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