Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Special Issue: New Trends in Infinite Dimensional Analysis and Quantum Probability
A Gauss-Poisson Correspondence and the Lévy Laplacian
Kimiaki SAITÔ
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2009 Volume 15 Issue 3 Pages 431-440

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Abstract

In this paper we present recent results on infinite dimensional Laplacians. In particular, by introducing the operator which transfers regular white noise functionals to functionals of exponential white noise, we give a relationship between an infinite dimensional Fourier-Mehler transform and the Lévy Laplacian. The operator implies a Gauss-Poisson correspondence if we consider the Lévy Laplacian acting on multiple Wiener integrals by some Lévy process. We also give an infinite dimensional random field associated with the Lévy Laplacian.

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© 2009 by the Graduate School of Information Sciences (GSIS), Tohoku University

This article is licensed under a Creative Commons [Attribution 4.0 International] license.
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