Uniqueness of solution to the Kolmogorov’s forward equation: Applications to White Noise Theory of Filtering
نویسندگان
چکیده
We consider a signal process X taking values in a complete, separable metric space E. X is assumed to be a Markov process charachterized via the martingale problem for an operator A. In the context of the finitely additive white noise theory of filtering, we show that the optimal filter Γt(y) is the unique solution of the analogue of the Zakai equation for every y, not necessarily continuous. This is done by first proving uniqueness of solution to a (perturbed) measure valued evolution equation associated with A. An additional assumption of uniqueness of the local martingale problem for A is imposed. AMS 2000 subject classification: Primary 60G35 Secondary 60J35, 60G44
منابع مشابه
Uniqueness of Solution to the Kolmogorov Forward Equation: Applications to White Noise Theory of Filtering
We consider a signal process X taking values in a complete, separable metric space E. X is assumed to be a Markov process charachterized via the martingale problem for an operator A. In the context of the finitely additive white noise theory of filtering, we show that the optimal filter Γt(y) is the unique solution of the analogue of the Zakai equation for every y, not necessarily continuous. T...
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