A Dynamic Programming Formulation for the Nonlinear Filter

2021/10/29 by Kim, Jin Won, Mehta, Prashant G.
#FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.00109

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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