QUASI-REGULAR DIRICHLET FORMS ON FREE RIEMANNIAN PATH SPACES

被引：7

作者：

Wang, Feng-Yu ^{[1
]}

Wu, Bo

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2009年 / 12卷 / 02期

关键词：

Quasi-regular Dirichlet form; free path space; integration by parts formula; CONSTRUCTION; DIFFUSIONS;

D O I：

10.1142/S0219025709003628

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The integration by parts formula on free path spaces over noncompact Riemannian manifolds is established for initial distributions with densities in W-loc(2,1). As an application, a large class of Dirichlet forms with (unbounded and non-constant) diffusion coefficients are constructed on free Riemannian path spaces, which are quasi-regular under mild curvature conditions.

引用

页码：251 / 267

页数：17

共 20 条

[1]

ALBEVERIO S, 1993, CR ACAD SCI I-MATH, V316, P287

[2]

[Anonymous], 1979, LECT NOTES MATH

[3] MARTINGALE REPRESENTATION AND A SIMPLE PROOF OF LOGARITHMIC SOBOLEV INEQUALITIES ON PATH SPACES [J].

Capitaine, Mireille ;

Hsu, Elton P. ;

Ledoux, Michel .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 1997, 2 :71-81

[4] A CAMERON-MARTIN TYPE QUASI-INVARIANCE THEOREM FOR BROWNIAN-MOTION ON A COMPACT RIEMANNIAN MANIFOLD [J].

DRIVER, BK .

JOURNAL OF FUNCTIONAL ANALYSIS, 1992, 110 (02) :272-376

[5]

DRIVER BK, 1992, CR ACAD SCI I-MATH, V315, P603

[6] Analysis on free Riemannian path spaces [J].

Fang, SZ ;

Wang, FY .

BULLETIN DES SCIENCES MATHEMATIQUES, 2005, 129 (04) :339-355

[7] Algebraic structure on Dirichlet spaces [J].

Fang, Xing ;

He, Ping ;

Ying, Jian Gang .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2006, 22 (03) :723-728

[8]

Fukushima M., 2011, De Gruyter Stud. Math., V19

[9] Quasi-invariance of the Wiener measure on the path space over a compact Riemannian manifold [J].

Hsu, EP .

JOURNAL OF FUNCTIONAL ANALYSIS, 1995, 134 (02) :417-450

[10] THE RADIAL PART OF BROWNIAN-MOTION ON A MANIFOLD - A SEMIMARTINGALE PROPERTY [J].

KENDALL, WS .

ANNALS OF PROBABILITY, 1987, 15 (04) :1491-1500

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