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The rate function of hypoelliptic diffusions
Author(s) -
Arous Gérard Ben,
Deuschel JeanDominique
Publication year - 1994
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160470604
Subject(s) - hypoelliptic operator , mathematics , affine transformation , measure (data warehouse) , order (exchange) , function (biology) , operator (biology) , diffusion , mathematical analysis , pure mathematics , manifold (fluid mechanics) , partial differential equation , linear differential equation , repressor , database , chemistry , computer science , engineering , biology , biochemistry , evolutionary biology , transcription factor , thermodynamics , mechanical engineering , physics , finance , economics , gene
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 L 0 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 X i 's, we derive an affine bound relating the rate functions associated with L and L 0 . As soon as one point exists where Y is not in the linear span of the first and second‐order Lie brackets of the X i 's, we show that such an affine bound is impossible. © 1994 John Wiley & Sons, Inc.