Electronic Journal of Probability

Nonlinear Filtering for Reflecting Diffusions in Random Enviroments via Nonparametric Estimation

Michael Kouritzin, Wei Sun, and Jie Xiong

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We study a nonlinear filtering problem in which the signal to be estimated is a reflecting diffusion in a random environment. Under the assumption that the observation noise is independent of the signal, we develop a nonparametric functional estimation method for finding workable approximate solutions to the conditional distributions of the signal state. Furthermore, we show that the pathwise average distance, per unit time, of the approximate filter from the optimal filter is asymptotically small in time. Also, we use simulations based upon a particle filter algorithm to show the efficiency of the method.

Article information

Electron. J. Probab. Volume 9 (2004), paper no. 18, 560-574.

Accepted: 12 July 2004
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60J60: Diffusion processes [See also 58J65] 60J65: Brownian motion [See also 58J65] 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

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Kouritzin, Michael; Sun, Wei; Xiong, Jie. Nonlinear Filtering for Reflecting Diffusions in Random Enviroments via Nonparametric Estimation. Electron. J. Probab. 9 (2004), paper no. 18, 560--574. doi:10.1214/EJP.v9-214. https://projecteuclid.org/euclid.ejp/1465229704

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