Annals of Probability

Weak Poincaré inequalities on domains defined by Brownian rough paths

Shigeki Aida

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Abstract

We prove weak Poincaré inequalities on domains which are inverse images of open sets in Wiener spaces under continuous functions of Brownian rough paths. The result is applicable to Dirichlet forms on loop groups and connected open subsets of path spaces over compact Riemannian manifolds.

Article information

Source
Ann. Probab., Volume 32, Number 4 (2004), 3116-3137.

Dates
First available in Project Euclid: 8 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1107883348

Digital Object Identifier
doi:10.1214/009117904000000478

Mathematical Reviews number (MathSciNet)
MR2094440

Zentralblatt MATH identifier
1067.60029

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]

Keywords
Weak Poincaré inequality Brownian rough path convexity logarithmic Sobolev inequality

Citation

Aida, Shigeki. Weak Poincaré inequalities on domains defined by Brownian rough paths. Ann. Probab. 32 (2004), no. 4, 3116--3137. doi:10.1214/009117904000000478. https://projecteuclid.org/euclid.aop/1107883348


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