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

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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
General Mathematics
Computational Theory and Mathematics

Access to Document

10.1007/BF01692071

Cite this

@article{17f103cf5a3d4c17b46e18b4f5613cc4,

title = "On the small time behavior of the nonlinear estimation problem for finite bandwidth signals",

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.",

author = "Thomas Taylor",

year = "1987",

month = dec,

day = "1",

doi = "10.1007/BF01692071",

language = "English (US)",

volume = "20",

pages = "283--303",

journal = "Mathematical Systems Theory",

issn = "0025-5661",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - On the small time behavior of the nonlinear estimation problem for finite bandwidth signals

AU - Taylor, Thomas

PY - 1987/12/1

Y1 - 1987/12/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0010166768&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010166768&partnerID=8YFLogxK

U2 - 10.1007/BF01692071

DO - 10.1007/BF01692071

M3 - Article

AN - SCOPUS:0010166768

SN - 0025-5661

VL - 20

SP - 283

EP - 303

JO - Mathematical Systems Theory

JF - Mathematical Systems Theory

IS - 1

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this