Quantitative Convergence of the Filter Solution for Multiple Timescale Nonlinear Systems with Coarse-Grain Correlated Noise

Autor:	Beeson, Ryne, Namachchivaya, N. Sri, Perkowski, Nicolas
Rok vydání:	2020
Předmět:	Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	In this paper we prove a rate of convergence for the continuous time filtering solution of a multiple timescale correlated nonlinear system to a lower dimensional filtering equation in the limit of large timescale separation. Correlation is assumed to occur between the slow signal and observation processes. Convergence is almost sure in the weak topology. An asymptotic expansion of the dual process for the solution to the Zakai equation, and probabilistic representation using backward doubly stochastic differential equations is leveraged to prove the result. Comment: 27 pages. arXiv admin note: text overlap with arXiv:2010.16401
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2011.12801 Zobrazit plný text záznamu View this record from Arxiv