On the Zakai equation of filtering with Gaussian noise

Leszek Gawarecki; Vidyadhar S. Mandrekar

doi:10.1007/978-1-4612-0167-0_8

On the Zakai equation of filtering with Gaussian noise

Leszek Gawarecki, Vidyadhar S. Mandrekar

Kettering University

Michigan State University

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

The purpose of this work is to present an analogue of the Zakai type equation in case the noise is a Gaussian process, including fractional Brownian motion (fBm). The problem is of interest in view of the fact that the signal sent through the internet is contaminated by the noise given by fBm ([6]). Recently, a similar filtering problem with fBm noise was considered in [1]. However, the authors considered a non—Markovian signal process. The assumption of the Markov property on the signal is realistic. This also leads to a recursive equation, which is easily tractable, and is widely studied ([11, 5]).

Original language	American English
Title of host publication	Stochastics in Finite and Infinite Dimensions
DOIs	https://doi.org/10.1007/978-1-4612-0167-0_8
State	Published - Jan 1 2001

Keywords

Brownian Motion
Fractional Brownian Motion
Reproduce Kernel Hilbert Space
Stochastic Partial Differential Equation
Martingale Problem

Disciplines

Mathematics

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10.1007/978-1-4612-0167-0_8License: CC BY

https://link.springer.com/chapter/10.1007/978-1-4612-0167-0_8

Cite this

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N2 - The purpose of this work is to present an analogue of the Zakai type equation in case the noise is a Gaussian process, including fractional Brownian motion (fBm). The problem is of interest in view of the fact that the signal sent through the internet is contaminated by the noise given by fBm ([6]). Recently, a similar filtering problem with fBm noise was considered in [1]. However, the authors considered a non—Markovian signal process. The assumption of the Markov property on the signal is realistic. This also leads to a recursive equation, which is easily tractable, and is widely studied ([11, 5]).

AB - The purpose of this work is to present an analogue of the Zakai type equation in case the noise is a Gaussian process, including fractional Brownian motion (fBm). The problem is of interest in view of the fact that the signal sent through the internet is contaminated by the noise given by fBm ([6]). Recently, a similar filtering problem with fBm noise was considered in [1]. However, the authors considered a non—Markovian signal process. The assumption of the Markov property on the signal is realistic. This also leads to a recursive equation, which is easily tractable, and is widely studied ([11, 5]).

KW - Brownian Motion

KW - Fractional Brownian Motion

KW - Reproduce Kernel Hilbert Space

KW - Stochastic Partial Differential Equation

KW - Martingale Problem

UR - https://digitalcommons.kettering.edu/mathematics_facultypubs/15

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DO - 10.1007/978-1-4612-0167-0_8

M3 - Chapter

BT - Stochastics in Finite and Infinite Dimensions

ER -

On the Zakai equation of filtering with Gaussian noise

Abstract

Keywords

Disciplines

Access to Document

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Cite this