## 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) |
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Pages (from-to) | 843-860 |

Number of pages | 18 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 47 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1994 |

## ASJC Scopus subject areas

- General Mathematics
- Applied Mathematics