A Large Deviation Principle for Martingales over Brownian Filtration
نویسندگان
چکیده
In this article we establish a large deviation principle for the family {ν ε : ε ∈ (0, 1)} of distributions of the scaled stochastic processes {P − log √ ε Z t } t≤1 , where (Z t) t∈[0,1] is a square-integrable martingale over Brownian filtration and (P t) t≥0 is the Ornstein-Uhlenbeck semigroup. The rate function is identified as well in terms of the Wiener-Itô chaos decomposition of the terminal value Z 1. The result is established by developing a continuity theorem for large deviations, together with two essential tools, the hypercontractivity of the Ornstein-Uhlenbeck semi-group and Lyons' continuity theorem for solutions of Stratonovich type stochastic differential equations.
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