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Non-linear filtering of rare events with large signal-to-noise ratio

Published online by Cambridge University Press:  14 July 2016

A. J. Heunis
A. J. Heunis*
Affiliation:
University of Waterloo
*
∗Postal address: Department of Electrical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
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Abstract

The theory of robust non-linear filtering in Clark (1978) and Davis (1980), (1982) is used to evaluate the limiting conditional distribution of a diffusion, given an observation of a ‘rare-event' sample-path of the diffusion, as the signal-to-noise ratio and the diffusion noise-intensity converge to infinity and zero respectively. Under mild conditions it is shown that the limiting conditional distribution is a Dirac measure concentrated at a trajectory which solves a variational problem parametrised by the sample-path of the observed signal.

Keywords

ROBUST NON-LINEAR FILTERDIFFUSIONSRARE EVENTSLARGE DEVIATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987 , pp. 929 - 948
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

This work was supported by the UK Science and Engineering Research Council, and by the Natural Sciences and Engineering Research Council of Canada.

References

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