A Support Theorem for the Filter under Infinite Dimensional Noise and Unbounded Observation Coefficients

A Support Theorem for the Filter under Infinite Dimensional Noise and Unbounded Observation... In this paper we consider a nonlinear filtering problem with an unbounded observation coefficient, correlated noises, and a signal process driven by an infinite dimensional Brownian motion. We prove that the unnormalized filter admits a smooth density which is in the Schwartz space and we give a description of the support of the law of this density. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

A Support Theorem for the Filter under Infinite Dimensional Noise and Unbounded Observation Coefficients

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Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 1999 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002459900109
Publisher site
See Article on Publisher Site

Abstract

In this paper we consider a nonlinear filtering problem with an unbounded observation coefficient, correlated noises, and a signal process driven by an infinite dimensional Brownian motion. We prove that the unnormalized filter admits a smooth density which is in the Schwartz space and we give a description of the support of the law of this density.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Feb 1, 2041

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