Kalman-Bucy filter and SPDEs with growing lower-order coefficients in \(W_{p}^{1}\) spaces without weights. (English) Zbl 1260.60122
Summary: 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, \(p \geq 2\), 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.
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 93E11 | Filtering in stochastic control theory |
References:
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