Generators of Brownian motions on abstract Wiener spaces

• Autorzy: Kei Harada
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 60J45: Probabilistic potential theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 89
• Numer: 1
• Strony: 135-142

Daty

wydano

2010

Twórcy

autor

Kei Harada

• Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan

Identyfikatory

DOI

10.4064/bc89-0-8