The Annals of Probability

Small-time Gaussian behavior of symmetric diffusion semi-groups

Masanori Hino and José A. Ramírez

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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.

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

First available in Project Euclid: 12 June 2003

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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]

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


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.

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