Annals of Probability

A Nonhomogeneous Markov Process for the Estimation of Gaussian Random Fields with Nonlinear Observations

Yali Amit and Mauro Piccioni

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Abstract

We consider an estimation problem in which the signal is modelled by a continuous Gaussian random field and is observed through smooth and bounded nonlinear sensors. A nonhomogeneous Markov process is defined in order to sample the conditional distribution of the signal given the observations. At any finite time the process takes values in a finite-dimensional space, although the dimension goes to infinity in time. We prove that the empirical averages of any bounded functional continuous w.p.1 converge in the mean square to the conditional expectation of the functional.

Article information

Source
Ann. Probab., Volume 19, Number 4 (1991), 1664-1678.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990228

Digital Object Identifier
doi:10.1214/aop/1176990228

Mathematical Reviews number (MathSciNet)
MR1127720

Zentralblatt MATH identifier
0739.60040

JSTOR
links.jstor.org

Subjects
Primary: 60G60: Random fields
Secondary: 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Gaussian random fields nonhomogeneous Markov processes estimation Galerkin approximations

Citation

Amit, Yali; Piccioni, Mauro. A Nonhomogeneous Markov Process for the Estimation of Gaussian Random Fields with Nonlinear Observations. Ann. Probab. 19 (1991), no. 4, 1664--1678. doi:10.1214/aop/1176990228. https://projecteuclid.org/euclid.aop/1176990228


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