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

摘要

Using a simple martingale representation result, a partial integration-by-parts formula is obtained. Quoting the results of Bismut and Michel, it then follows that under Hoermander's conditions on the coefficient vector fields, the filtering, smoothing and prediction problems have C at infinity density solutions. The paper does not require the development of any analysis over Wiener space. Reprints. (JHD)