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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465229704

Digital Object Identifier
doi:10.1214/EJP.v9-214

Mathematical Reviews number (MathSciNet)
MR2080609

Zentralblatt MATH identifier
1065.60151

Subjects
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]

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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