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We present several results on the smoothness in $L_{p}$ sense of filteringdensities under the Lipschitz continuity assumption on the coefficients of apartially observable diffusion processes. We obtain them by rewriting indivergence form filtering equation which are usually considered in terms offormally adjoint to operators in nondivergence form.

SPDEs in divergence form with VMO coefficients and filtering theory of partially observable diffusion processes with Lipschitz coefficients