Annals of Probability

Weak Poincaré inequalities on domains defined by Brownian rough paths

Shigeki Aida

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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

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

First available in Project Euclid: 8 February 2005

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Zentralblatt MATH identifier

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]

Weak Poincaré inequality Brownian rough path convexity logarithmic Sobolev inequality


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

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