On the Semi-classical Brownian Bridge Measure

被引：6

作者：

Li, Xue-Mei ^{[1
]}

机构：

[1] Univ Warwick, Math Inst, Warsaw, Poland

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2017年 / 22卷

关键词：

Malliavin calculus; pinned path spaces; loop spaces; integration by parts; Poincare inequality; LOGARITHMIC SOBOLEV INEQUALITIES; QUASI-INVARIANCE THEOREM; PINNED WIENER MEASURE; HEAT KERNEL MEASURE; HARMONIC-FUNCTIONS; SPECTRAL GAPS; LOOP-SPACES; INTEGRATION; UNIQUENESS; EQUATION;

D O I：

10.1214/17-ECP69

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove an integration by parts formula for the probability measure on the pinned path space induced by the Semi-classical Riemmanian Brownian Bridge, over a manifold with a pole, followed by a discussion on its equivalence with the Brownian Bridge measure.

引用

页数：15

共 41 条

[1] Precise Gaussian estimates of heat kernels on asymptotically flat Riemannian manifolds with poles
Aida, S
[J]. RECENT DEVELOPMENTS IN STOCHASTIC ANALYSIS AND RELATED TOPICS, 2004, : 1 - 19
[2] Equivalence of heat kernel measure and pinned Wiener measure on loop groups
Aida, S
Driver, BK
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 331 (09): : 709 - 712
[3] Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces
Aida, S
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 174 (02) : 430 - 477
[4] Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds
Aida, Shigeki
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2015, 269 (12) : 3714 - 3764
[5] INTEGRATION ON LOOP-GROUPS .2. HEAT-EQUATION FOR THE WIENER MEASURE
AIRAULT, H
MALLIAVIN, P
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1992, 104 (01) : 71 - 109
[6] [Anonymous], ARXIV161009538
[7] [Anonymous], 1979, LECT NOTES MATH
[8] [Anonymous], PREPRINT
[9] Gradient estimates for positive harmonic functions by stochastic analysis
Arnaudon, Marc
Driver, Bruce K.
Thalmaier, Anton
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2007, 117 (02) : 202 - 220
[10] Chen X., QUASI REGULAR DIRICH

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