### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 843-860 |

Number of pages | 18 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 47 |

Issue number | 6 |

DOIs | |

State | Published - 1994 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*47*(6), 843-860. https://doi.org/10.1002/cpa.3160470604

**The rate function of hypoelliptic diffusions.** / Ben Arous, Gerard; Deuschel, Jean‐Dominique ‐D.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 47, no. 6, pp. 843-860. https://doi.org/10.1002/cpa.3160470604

}

TY - JOUR

T1 - The rate function of hypoelliptic diffusions

AU - Ben Arous, Gerard

AU - Deuschel, Jean‐Dominique ‐D

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84990727081&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990727081&partnerID=8YFLogxK

U2 - 10.1002/cpa.3160470604

DO - 10.1002/cpa.3160470604

M3 - Article

VL - 47

SP - 843

EP - 860

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 6

ER -