Generators of Brownian motions on abstract Wiener spaces

Kei Harada. "Generators of Brownian motions on abstract Wiener spaces." Banach Center Publications 89.1 (2010): 135-142. <http://eudml.org/doc/281642>.

@article{KeiHarada2010,
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.},
author = {Kei Harada},
journal = {Banach Center Publications},
keywords = {Gross Laplacian; -topology; heat equation in infinite dimensions},
language = {eng},
number = {1},
pages = {135-142},
title = {Generators of Brownian motions on abstract Wiener spaces},
url = {http://eudml.org/doc/281642},
volume = {89},
year = {2010},
}

TY - JOUR
AU - Kei Harada
TI - Generators of Brownian motions on abstract Wiener spaces
JO - Banach Center Publications
PY - 2010
VL - 89
IS - 1
SP - 135
EP - 142
AB - 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.
LA - eng
KW - Gross Laplacian; -topology; heat equation in infinite dimensions
UR - http://eudml.org/doc/281642
ER -