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 languageEnglish (US)
Pages (from-to)283-303
Number of pages21
JournalMathematical Systems Theory
Volume20
Issue number1
DOIs
StatePublished - Dec 1987

Fingerprint

Zakai Equation
Nonlinear Estimation
Bandwidth
Partial differential equations
Wave equations
Stochastic Partial Differential Equations
Behavior of Solutions
Wave equation
Partial differential equation
Transform

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics(all)
  • Computational Theory and Mathematics

Cite this

On the small time behavior of the nonlinear estimation problem for finite bandwidth signals. / Taylor, Thomas.

In: Mathematical Systems Theory, Vol. 20, No. 1, 12.1987, p. 283-303.

Research output: Contribution to journalArticle

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