Robustness of the nonlinear filter: the correlated case

Bhatt, Abhay G. ; Karandikar, Rajeeva L. (2002) Robustness of the nonlinear filter: the correlated case Stochastic Processes and their Applications, 97 (1). pp. 41-58. ISSN 0304-4149

PDF - Publisher Version

Official URL:

Related URL:


We consider the question of robustness of the optimal nonlinear filter when the signal process X and the observation noise are possibly correlated. The signal X and observations Y are given by a SDE where the coefficients can depend on the entire past. Using results on pathwise solutions of stochastic differential equations we express X as a functional of two independent Brownian motions under the reference probability measure P0. This allows us to write the filter p as a ratio of two expectations. This is the main step in proving robustness. In this framework we show that when (Xn,Yn) converge to (X,Y) in law, then the corresponding filters also converge in law. Moreover, when the signal and observation processes converge in probability, so do the filters. We also prove that the paths of the filter are continuous in this framework.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Nonlinear Filtering; Correlated Signal and Noise; Robustness; Pathwise Formulae for SDE
ID Code:18408
Deposited On:17 Nov 2010 09:15
Last Modified:17 May 2016 03:08

Repository Staff Only: item control page