Existence of Smooth Densities for the Prediction, Filtering and Smoothing Problems.

摘要

Stochastic flows are used to derive martingale representation results and formulae for integration by parts in function space. In turn, these give results on the existence of densities for filtering, smoothing, and prediction problems. Stochastic flows are also used to derive minimum principles in stochastic control, and new equations for the adjoint process. Related results are also obtained for jump processes and the control of Markov chains. Martingale representation results are used to minimize expected risk. Using integration by parts, reverse time representations of jump processes are obtained. These results have applications in, for example, smoothing and the Malliavin calculus.