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Seminar on Stochastic Analysis, Random Fields and Applications VIExponential Integrability and DLR Consistence of Some Rough Functionals

Seminar on Stochastic Analysis, Random Fields and Applications VI: Exponential Integrability and... [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Seminar on Stochastic Analysis, Random Fields and Applications VIExponential Integrability and DLR Consistence of Some Rough Functionals

Part of the Progress in Probability Book Series (volume 63)
Editors: Dalang, Robert; Dozzi, Marco; Russo, Francesco

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References (55)

Publisher
Springer Basel
Copyright
© Springer Basel AG 2011
ISBN
978-3-0348-0020-4
Pages
191 –208
DOI
10.1007/978-3-0348-0021-1_13
Publisher site
See Chapter on Publisher Site

Abstract

[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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