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Generators of Brownian motions on abstract Wiener spaces

Tom 89 / 2010

Kei Harada Banach Center Publications 89 (2010), 135-142 MSC: 47D06, 60J45. DOI: 10.4064/bc89-0-8

Streszczenie

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.

Autorzy

  • Kei HaradaGraduate School of Mathematics
    Nagoya University
    Nagoya 464-8602, Japan
    e-mail

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