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Green functions and the support of hypoelliptic diffusions

Abstract : The first part contains a precise description of the singularity
near the diagonal of the Green function associated to a hypoelliptic
operator. Our approach is probabilistic and relies on the stochastic
Taylor expansion of paths of the associated diffusion and on a
priori estimates of the Green function. Examples and applications
to potential theory are given.
In the second part one extends the Stroock-Varadhan support theorem
for Hölder norms. The central tool is an estimate of the
probability that the Brownian motion has a large Hölder norm
conditionally on the fact that it has a small uniform norm.
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Contributor : Mihai Gradinaru <>
Submitted on : Wednesday, March 8, 2006 - 1:46:06 PM
Last modification on : Saturday, January 26, 2019 - 1:21:23 AM
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  • HAL Id : tel-00011820, version 1



Mihai Gradinaru. Green functions and the support of hypoelliptic diffusions. Mathematics [math]. Université Paris Sud - Paris XI, 1995. English. ⟨tel-00011820⟩



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