Pathwise stochastic control with applications to robust filtering (Q2657939)

The authors propose a new approach to robust filtering for time continuous stochastic systems described by stochastic differential equations. The line of reasoning follows the one describes in [\textit{A. L. Allan} and \textit{S. N. Cohen}, SIAM J. Control Optim. 57, No. 3, 1646--1671 (2019; Zbl 1420.62407)] where a nonlinear expectation described in terms of a penalty function is used. Nevertheless by relaxing some assumptions of [loc. cit.] the authors propose a more general penalty which allows to take into account the statistical likelihood for different parameter choices. It leads to the derivation of a pathwise stochastic control problem which is solved by the rough path theory introduced in [\textit{T. J. Lyons}, Rev. Mat. Iberoam. 14, No. 2, 215--310 (1998; Zbl 0923.34056)] and developed in [\textit{J. Diehl} et al., Appl. Math. Optim. 75, No. 2, 285--315 (2017; Zbl 1373.60099)]. To ensure that a dynamic programming machinery is retained the authors introduce an artificial penalty function which allows to constrain variation of the controls. A side effect of this idea is a solution to a problem with unbounded cost functions in which local uniform bounds on the control enables the unique solution of a rough Hamilton-Jacobi-Bellman partial differential equation.