Generators of Brownian motions on abstract Wiener spaces
Volume 89 / 2010
Banach Center Publications 89 (2010), 135-142
MSC: 47D06, 60J45.
DOI: 10.4064/bc89-0-8
Abstract
We prove that Brownian motion on an abstract Wiener space $B$ generates a locally equicontinuous semigroup on $C_b(B)$ equipped with the $T_t$-topology introduced by L. Le Cam. Hence we obtain a “Laplace operator” as its infinitesimal generator. Using this Laplacian, we discuss Poisson's equation and heat equation, and study its properties, especially the difference from the Gross Laplacian.
