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Asymptotic stability of the optimal filter for random chaotic maps

Bröcker, J. and Del Magno, G. (2017) Asymptotic stability of the optimal filter for random chaotic maps. Nonlinearity, 30 (5). pp. 1809-1833. ISSN 1361-6544

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To link to this item DOI: 10.1088/1361-6544/aa639c

Abstract/Summary

The asymptotic stability of the optimal filtering process in discrete time is revisited. The filtering process is the conditional probability of the state of a Markov process, called the signal process, given a series of observations. Asymptotic stability means that the distance between the true filtering process and a wrongly initialised filter converges to zero as time progresses. In the present setting, the signal process arises through iterating an i.i.d. sequence of uniformly expanding random maps. It is showed that for such a signal, the asymptotic stability is exponential provided that its initial conditions are sufficiently smooth. Similar to previous work on this problem, Hilbert’s projective metric on cones is employed as well as certain mixing properties of the signal, albeit with important differences. Mixing and ultimately filter stability in the present situation are due to the expanding dynamics rather than the stochasticity of the signal process. In fact, the conditions even permit iterations of a fixed (nonrandom) expanding map.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:69444
Publisher:Institute of Physics

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