## An introduction to the theory of large deviations |

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### Contents

Introduction j 1 Brownian Motion in Small Time Strassens Iterated Logarithm | 2 |

Large Deviations Some Generalities | 23 |

Cramers Theorem | 30 |

Copyright | |

6 other sections not shown

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### Common terms and phrases

absolutely continuous assume bounded Brownian motion Cb(E centered Gaussian Cfe(E choose Clearly closed convex closed F closed sets convergence convex function convex rate function convex set Corollary define E X[exp epi(f ergodic exists Finally finite Gaussian measure Given Hence Ia(v implies inf J(v inf Q inf X(x inf{t large deviation principle Lemma Let f lim e log lim sup log Q log u F log2 lower semi-continuous LP(m Lq(m lxl_ Markov property martingale Moreover non-decreasing open convex open G open set particular Polish space preceding principle with rate probability measure random variables rate function result satisfies the large semigroup separable Banach space Sobolev inequalities sub-additive subset sup lp(t)l sup Q suppose t x€E Theorem tight transition function u(dx unique v(dx Varadhan xE(t YE(t