Exponential stability in discrete-time filtering for non-ergodic signals

A. Budhiraja and D. Ocone

Stochastic Processes and their Applications, 1999, vol. 82, issue 2, 245-257

Abstract: In this paper we prove exponential asymptotic stability for discrete-time filters for signals arising as solutions of d-dimensional stochastic difference equations. The observation process is the signal corrupted by an additive white noise of sufficiently small variance. The model for the signal admits non-ergodic processes. We show that almost surely, the total variation distance between the optimal filter and an incorrectly initialized filter converges to 0 exponentially fast as time approaches [infinity].

Keywords: Nonlinear; filtering; Asymptotic; stability; Measure; valued; processes (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (5)

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