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Online sequential Monte Carlo smoother for partially observed diffusion processes

By Pierre Gloaguen, Marie-Pierre √Čtienne and Sylvain Le Corff

Abstract

Abstract This paper introduces a new algorithm to approximate smoothed additive functionals of partially observed diffusion processes. This method relies on a new sequential Monte Carlo method which allows to compute such approximations online, i.e., as the observations are received, and with a computational complexity growing linearly with the number of Monte Carlo samples. The original algorithm cannot be used in the case of partially observed stochastic differential equations since the transition density of the latent data is usually unknown. We prove that it may be extended to partially observed continuous processes by replacing this unknown quantity by an unbiased estimator obtained for instance using general Poisson estimators. This estimator is proved to be consistent and its performance are illustrated using data from two models

Topics: Stochastic differential equations, Smoothing, Sequential Monte Carlo Methods, Online estimation, Telecommunication, TK5101-6720, Electronics, TK7800-8360
Publisher: SpringerOpen
Year: 2018
DOI identifier: 10.1186/s13634-018-0530-3
OAI identifier: oai:doaj.org/article:9d89622164c94796b68609bd047a7308
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