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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
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.
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- Copyright © Applied Probability Trust 1987
Footnotes
This work was supported by the UK Science and Engineering Research Council, and by the Natural Sciences and Engineering Research Council of Canada.
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