Kalman-Bucy filter and spdes with growing lower-order coefficients in W1 p spaces without weights

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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 pth 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.

Original languageEnglish (US)
Pages (from-to)1069-1114
Number of pages46
JournalIllinois Journal of Mathematics
Issue number3
StatePublished - 2010

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