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

Electronic Journal of Differential Equations

article

Richard C. Penney¹  Roman Urban² 

[1] Department of Mathematics Purdue University 150 N. University St West Lafayette;Institute of Mathematics Wroclaw University Plac Grunwaldzki 2/4 50-384 Wroclaw

关键词: Poisson measure;    Gaussian measure;    Hilbert space;    Brownian motion;    evolution kernel;    diffusion processes.;   

DOI  :  10.58997/ejde.2022.04

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

Let "$G=X\rtimes A$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.

【 授权许可】

CC BY