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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 density 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 in terms of stochastic characteristics has been proved by Krylov and Rozovskii and by Kunita. A discretization scheme is then provided to approximate these stochastic characteristics. Under the additional assumption that the correlation coefficient is constant, 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.
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https://hal.inria.fr/hal-00912048
Contributor : Francois Le Gland <>
Submitted on : Monday, December 2, 2013 - 12:59:20 AM
Last modification on : Friday, July 9, 2021 - 11:30:44 AM

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Patrick Florchinger, François Le Gland. Time discretization of the Zakai equation for diffusion processes observed in correlated noise. Stochastics and Stochastics Reports, Informa UK (Taylor & Francis), 1991, 35 (4), pp.233-256. ⟨10.1080/17442509108833704⟩. ⟨hal-00912048⟩

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