A Dynamic Programming Formulation for the Nonlinear Filter

Jin Won Kim; Prashant G. Mehta

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arXiv · 2111.00109

A Dynamic Programming Formulation for the Nonlinear Filter

Jin Won Kim·Prashant G. Mehta

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Abstract

This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The solution is obtained via an application of the maximum principle (MP). In the present paper, a dynamic programming (DP) principle is presented for a special class of BSDE-constrained stochastic optimal control problems. The principle is applied to derive the solution of the nonlinear filtering problem.

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Jin Won Kim, Prashant G. Mehta. 2021-10-29. A Dynamic Programming Formulation for the Nonlinear Filter. https://arxiv.org/abs/2111.00109

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