The Annals of Probability

Small-time Gaussian behavior of symmetric diffusion semi-groups

Masanori Hino and José A. Ramírez

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Abstract

This work is involved with the short-time asymptotics of diffusion semigroups in a general setting. A generalization of Fang's version of Varadhan's formula is proven for general Dirichlet spaces that are local and conservative. The intrinsic metric appearing in the formula is characterized by pointwise distance for canonical Dirichlet spaces on loop groups.

Article information

Source
Ann. Probab., Volume 31, Number 3 (2003), 1254-1295.

Dates
First available in Project Euclid: 12 June 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1055425779

Digital Object Identifier
doi:10.1214/aop/1055425779

Mathematical Reviews number (MathSciNet)
MR1988472

Zentralblatt MATH identifier
1085.31008

Subjects
Primary: 31C25: Dirichlet spaces 60J60: Diffusion processes [See also 58J65] 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}
Secondary: 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]

Keywords
Dirichlet spaces heat kernel short-time asymptotics intrinsic metric loop group.

Citation

Hino, Masanori; Ramírez, José A. Small-time Gaussian behavior of symmetric diffusion semi-groups. Ann. Probab. 31 (2003), no. 3, 1254--1295. doi:10.1214/aop/1055425779. https://projecteuclid.org/euclid.aop/1055425779


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  • ITHACA, NEW YORK 14853 E-MAIL: ramirez@poly gon.math.cornell.edu