 Robustness of the nonlinear filter: the correlated caseAbhay G. Bhatt and Rajeeva L. Karandikar Stochastic Processes and their Applications, 2002, vol. 97, issue 1, 41-58 Abstract: 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 [pi] 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. Keywords: Nonlinear; filtering; Correlated; signal; and; noise; Robustness; Pathwise; formulae; for; SDE (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:97:y:2002:i:1:p:41-58 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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