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[First we review types of path measures arising from various extensions of the Feynman-Kac formula. Then we consider more closely the case of Gibbs measures on Brownian paths with respect to densities dependent on double Itô integrals. We explain the framework of stochastic currents used in order to give a sensible meaning to Gibbs specifications. Exponential integrability and DLR consistence will be established by using rough paths techniques. Finally we show the results on existence, uniqueness, typical path behaviour and mixing properties that can be derived for limit Gibbs random fields.]
Published: Feb 4, 2011
Keywords: Gibbs measure on path space; rough paths; stochastic currents
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