A Large Deviation Principle for Martingales over Brownian Filtration

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dc.creatorQian, Z.
dc.creatorXu, C.
dc.date2009-04-03
dc.date.accessioned2026-07-07T13:00:16Z
dc.date.available2026-07-07T13:00:16Z
dc.descriptionIn this article we establish a large deviation principle for the family {ν_ε:ε\in (0,1)} of distributions of the scaled stochastic processes {P_{-\log\sqrtε}Z_t}_{t\leq 1}, where (Z_t)_{t\in \lbrack 0,1]} is a square-integrable martingale over Brownian filtration and (P_t)_{t\geq 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 semigroup and Lyons' continuity theorem for solutions of Stratonovich type stochastic differential equations.
dc.description47 pages
dc.identifierhttps://arxiv.org/abs/0904.0547
dc.identifierhttp://arxiv.org/abs/0904.0547
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/225798
dc.subjectProbability
dc.subject60Hxx
dc.titleA Large Deviation Principle for Martingales over Brownian Filtration
dc.typetext

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