Finite-dimensional risk-sensitive filtering for continuous-time nonlinear systems

Risk-sensitive filtering results are obtained for a class of continuous-time nonlinear stochastic signal models. A modified Zakai equation is obtained for the risk-sensitive information state and an expression for the optimizing risk-sensitive estimate is given. It is shown that if the drift function in the state space model satisfies a certain partial differential equation involving the risk-sensitive cost-kernel, finite-dimensional risk-sensitive information states and filters can be obtained for quite general nonlinear drift functions. Brief discussions on small noise limit results and possible extensions are also included.