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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2008

On the linear-exponential filtering problem for general Gaussian processes

Résumé

The explicit solution of the filtering problem with exponential criteria for a general Gaussian signal is obtained through an approach which is based on a conditional Cameron-Martin-type formula. This key formula is derived for conditional expectations of exponentials of some quadratic functionals of a general continuous Gaussian process. The formula involves conditional expectations and conditional covariances in some auxiliary optimal risk-neutral filtering problem which is used in the proof. Closed form equations of the Itô-Volterra- and Riccati-Volterra-types for these ingredients are provided. Particular cases for which the results can be further elaborated are investigated.
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Dates et versions

hal-00853124 , version 1 (22-08-2013)

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Marina L. Kleptsyna, Alain Le Breton, Michel Viot. On the linear-exponential filtering problem for general Gaussian processes. SIAM Journal on Control and Optimization, 2008, 47 (6), pp.2886-2911. ⟨10.1137/070705908⟩. ⟨hal-00853124⟩
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