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Gaussian integrals on Wiener spaces

Part of: Markov processes Set functions and measures on spaces with additional structure Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Adam D. Helfer  and
Zhongxin Zhao
Adam D. Helfer
Affiliation:
University of Missouri
Zhongxin Zhao
Affiliation:
University of Missouri
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Abstract

We consider integrals on Wiener space of the forms E(exp K(x)) and E(exp K(x) |L(x) = l) where K is a quadratic form and L a system of linear forms. We give explicit formulas for these integrals in terms of the operators K and L, in the case that these arise from quasilinear functions in the sense of Zhao (1981). As examples, we recover Lévy's area formula in the plane, and derive new formulas for the probability density of the radius of gyration tensor for Brownian paths.

Keywords

ABSTRACT WIENER SPACESGAUSSIAN INTEGRALSSHAPE OF BROWNIAN PATHSSTOCHASTIC AREA

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G35: Signal detection and filtering 60J65: Brownian motion 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 46 - 55
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

∗

Postal address for both authors: Department of Mathematics, University of Missouri, Columbia, MO 65211, USA.

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