Malliavin calculus with time dependent coefficients and application to nonlinear filtering
Tóm tắt
In this paper, we prove, using Malliavin calculus, that under a local Hörmander condition the solution of a stochastic differential equation with time depending coefficients admits aC
∞ density with respect to Lebesgue measure. An application of this result to nonlinear filtering is developed in this paper to prove the existence of aC
∞ density for the filter associated with a correlated system whose observation is one dimensional with unbounded coefficients.
Tài liệu tham khảo
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