Time discretization of the Zakai equation for diffusion processes observed in correlated noise

Abstract : A time discretization scheme is provided for the Zakai equation, a stochastic PDE which gives the conditional law of a diffusion process observed in white-noise. The case where the observation noise and the state noise are correlated, is considered. The numerical scheme is based on a Trotter-like product formula, which exhibits prediction and correction steps, and for which an error estimate of order δ is proved, where δ is the time discretization step. The correction step is associated with a degenerate second-order stochastic PDE, for which a representation result is available in terms of stochastic characteristics. A discretization scheme is then provided to approximate these stochastic characteristics. Under an additional assumption on the correlation coefficient, an error estimate of order √δ is proved for the overall numerical scheme. This has been proved to be the best possible error estimate by Elliott and Glowinski.
Type de document :
Chapitre d'ouvrage
Bensoussan, Alain and Lions, Jacques―Louis. Analysis and Optimization of Systems, Antibes 1990, 144, Springer, pp.228-237, 1990, Lecture Notes in Control and Information Sciences, 〈10.1007/BFb0120045〉
Liste complète des métadonnées

https://hal.inria.fr/hal-00912046
Contributeur : Francois Le Gland <>
Soumis le : lundi 2 décembre 2013 - 01:04:50
Dernière modification le : jeudi 11 janvier 2018 - 16:39:51

Identifiants

Citation

Patrick Florchinger, François Le Gland. Time discretization of the Zakai equation for diffusion processes observed in correlated noise. Bensoussan, Alain and Lions, Jacques―Louis. Analysis and Optimization of Systems, Antibes 1990, 144, Springer, pp.228-237, 1990, Lecture Notes in Control and Information Sciences, 〈10.1007/BFb0120045〉. 〈hal-00912046〉

Partager

Métriques

Consultations de la notice

150