Poisson measures on semi-direct products of infinite-dimensional Hilbert spaces

Date

2022-01-10

Authors

Penney, Richard C.
Urban, Roman

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

Let G = X ⋊ A where X and A are Hilbert spaces considered as additive groups and the A-action on G is diagonal in some orthonormal basis. We consider a particular second order left-invariant differential operator L on G which is analogous to the Laplacian on ℝn. We prove the existence of "heat kernel" for L and give a probabilistic formula for it. We then prove that X is a "Poisson boundary" in a sense of Furstenberg for L with a (not necessarily) probabilistic measure ν on X called the "Poisson measure" for the operator L.

Description

Keywords

Poisson measure, Gaussian measure, Hilbert space, Brownian motion, Evolution kernel, Diffusion processes

Citation

Penney, R. C., & Urban, R. (2022). Poisson measures on semi-direct products of infinite-dimensional Hilbert spaces. <i>Electronic Journal of Differential Equations, 2022</i>(04), pp. 1-15.

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Attribution 4.0 International

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