Summary
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.
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Florchinger, P. Malliavin calculus with time dependent coefficients and application to nonlinear filtering. Probab. Th. Rel. Fields 86, 203–223 (1990). https://doi.org/10.1007/BF01474642
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DOI: https://doi.org/10.1007/BF01474642
Keywords
- Differential Equation
- Stochastic Process
- Probability Theory
- Lebesgue Measure
- Mathematical Biology