Title :
Existence of a density for the filter associated to Hilbert-space valued systems
Author :
Dietsch, Marie-noelle
Author_Institution :
Dept. de Math., Metz Univ., France
Abstract :
The purpose of this paper is to prove that the unnormalized filter associated to a Hilbert space valued nonlinear filtering problem with correlated noises, which solves a parabolic stochastic partial differential equation, the Zakai equation, admits a density with respect to a given measure on the Hilbert space. We also compute the stochastic differential equation solved by this density
Keywords :
Hilbert spaces; correlation methods; filtering theory; noise; nonlinear filters; parabolic equations; partial differential equations; Hilbert-space valued systems; correlated noises; nonlinear filtering problem; parabolic stochastic partial differential equation; unnormalized filter; Density measurement; Differential equations; Extraterrestrial measurements; Filtering; Filters; Hilbert space; Noise measurement; Nonlinear equations; Partial differential equations; Stochastic resonance;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2001.914574
