The rate function of hypoelliptic diffusions

Gérard Ben Arous, Jean‐Dominique ‐D Deuschel

Research output: Contribution to journalArticlepeer-review

Abstract

Let be a hypoelliptic diffusion operator on a compact manifold M. Given an a priori smooth reference measure λ on M, we can then rewrite L as the sum of a λ‐symmetric part L0 and a first‐order drift part Y. The paper investigates the effect of the drift Y on the Donsker‐Varadhan rate function corresponding to the large deviations of the empirical measure of the diffusion. When Y is in the linear span of the first and second‐order Lie brackets of the Xi's, we derive an affine bound relating the rate functions associated with L and L0. As soon as one point exists where Y is not in the linear span of the first and second‐order Lie brackets of the Xi's, we show that such an affine bound is impossible. © 1994 John Wiley & Sons, Inc.

Original languageEnglish (US)
Pages (from-to)843-860
Number of pages18
JournalCommunications on Pure and Applied Mathematics
Volume47
Issue number6
DOIs
StatePublished - Jun 1994

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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