On the small time behavior of the nonlinear estimation problem for finite bandwidth signals

Thomas Taylor

doi:10.1007/BF01692071

On the small time behavior of the nonlinear estimation problem for finite bandwidth signals

Thomas Taylor

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Abstract

In this paper we investigate the small time behavior of solutions of the Zakai equation. We derive a wave equation-like stochastic partial differential equation which is related to the Zakai equation. We are able to solve this equation for sufficiently smooth signals, and (approximately) transform these into solutions of the Zakai equation. We construct a Hadamardtype expansion for solutions of this partial differential equation and show how this expansion is related to a small time expansion of solutions of the Zakai equation.

Original language	English (US)
Pages (from-to)	283-303
Number of pages	21
Journal	Mathematical Systems Theory
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/BF01692071
State	Published - Dec 1 1987

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics(all)
Computational Theory and Mathematics

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10.1007/BF01692071

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abstract = "In this paper we investigate the small time behavior of solutions of the Zakai equation. We derive a wave equation-like stochastic partial differential equation which is related to the Zakai equation. We are able to solve this equation for sufficiently smooth signals, and (approximately) transform these into solutions of the Zakai equation. We construct a Hadamardtype expansion for solutions of this partial differential equation and show how this expansion is related to a small time expansion of solutions of the Zakai equation.",

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AB - In this paper we investigate the small time behavior of solutions of the Zakai equation. We derive a wave equation-like stochastic partial differential equation which is related to the Zakai equation. We are able to solve this equation for sufficiently smooth signals, and (approximately) transform these into solutions of the Zakai equation. We construct a Hadamardtype expansion for solutions of this partial differential equation and show how this expansion is related to a small time expansion of solutions of the Zakai equation.

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On the small time behavior of the nonlinear estimation problem for finite bandwidth signals

Abstract

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