Filtering problems with exponential criteria for general Gaussian signals
Probability
2009-12-14 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0908.2960,
title = {Filtering problems with exponential criteria for general Gaussian signals},
author = {M. L. Kleptsyna and A. Le Breton and M. Viot},
journal= {arXiv preprint arXiv:0908.2960},
year = {2009}
}
Comments
34 pages