On the Feynman-Kac formula and its applications to filtering theory |
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| Authors: | Rajeeva L. Karandikar |
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| Affiliation: | (1) Center for Stochastic Processes, University of North Carolina, Chapel Hill, 27514, NC, USA;(2) Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, 110016 New Delhi, India |
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| Abstract: | In this article the Feynman-Kac formula is obtained for a Markov process (Xt) whose transition probability function is not stationary. A converse to the Feynman-Kac formula is also obtained. This is used to prove the uniqueness of the solution to a measure-valued equation satisfied by the optimal filter in the white-noise approach to nonlinear filtering theory.Research partially supported by the Air Force Office of Scientific Research Contract No. F49620 85 C 0144 and by the Indian Statistical Institute. |
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