Generators of Brownian motions on abstract Wiener spaces

Kei Harada

Kei Harada

Banach Center Publications, Tome 89 (2010), p. 135-142 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Publié le : 2010-01-01

Zbl 1225.47041

EUDML-ID : urn:eudml:doc:281642

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     author = {Kei Harada},
     title = {Generators of Brownian motions on abstract Wiener spaces},
     journal = {Banach Center Publications},
     volume = {89},
     year = {2010},
     pages = {135-142},
     zbl = {1225.47041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-8}
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Kei Harada. Generators of Brownian motions on abstract Wiener spaces. Banach Center Publications, Tome 89 (2010) pp. 135-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-8/