Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 3, Pages 215-226
doi:10.1155/S104895330100017X
Abstract
The optimal filtering problem for multidimensional continuous possibly
non-Markovian, Gaussian processes, observed through a linear channel
driven by a Brownian motion, is revisited. Explicit Volterra type filtering
equations involving the covariance function of the filtered process are derived both for the conditional mean and for the covariance of the filtering
error. The solution of the filtering problem is applied to obtain a
Cameron-Martin type formula for Laplace transforms of a quadratic functional of the process. Particular cases for which the results can be further
elaborated are investigated.