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Gaussian integrals on Wiener spaces
Published online by Cambridge University Press: 14 July 2016
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.
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- Copyright © Applied Probability Trust 1992
Footnotes
Postal address for both authors: Department of Mathematics, University of Missouri, Columbia, MO 65211, USA.
References
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