Filtering problems with exponential criteria for general Gaussian signals

Details Filtering problems with exponential criteria for general Gaussian signals Filtering problems with exponential criteria for general Gaussian signals

2009-08-20

arxiv.org/abs/0908.2960v2

Mathematics

Probability

34 pages

Scientific paper

The explicit solution of the discrete time filtering problems with exponential criteria for a general Gaussian signal is obtained through an approach based on a conditional Cameron-Martin type formula. This key formula is derived for conditional expectations of exponentials of some quadratic forms of Gaussian sequences. The formula involves conditional expectations and conditional covariances in some auxiliary optimal risk-neutral filtering problem which is used in the proof. Closed form recursions of Volterra type for these ingredients are provided. Particular cases for which the results can be further elaborated are investigated.

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