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October, 1991 A Nonhomogeneous Markov Process for the Estimation of Gaussian Random Fields with Nonlinear Observations
Yali Amit, Mauro Piccioni
Ann. Probab. 19(4): 1664-1678 (October, 1991). DOI: 10.1214/aop/1176990228

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.

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Yali Amit. Mauro Piccioni. "A Nonhomogeneous Markov Process for the Estimation of Gaussian Random Fields with Nonlinear Observations." Ann. Probab. 19 (4) 1664 - 1678, October, 1991. https://doi.org/10.1214/aop/1176990228

Information

Published: October, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0739.60040
MathSciNet: MR1127720
Digital Object Identifier: 10.1214/aop/1176990228

Subjects:
Primary: 60G60
Secondary: 60H15

Keywords: estimation , Galerkin approximations , Gaussian random fields , nonhomogeneous Markov processes

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 4 • October, 1991
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