A characterization of Gibbs measures on \(C(0,1)^{\mathbb{Z}^ d}\) by the stochastic calculus of variations

zbMath0798.60090MaRDI QIDQ1322928

Hans Zessin, Sylvie Roelly

Publication date: 1 November 1994

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPB_1993__29_3_327_0

zbMATH Keywords

Sobolev spaceequilibrium measureGibbs measuresstochastic integralWiener measuresHamiltonian potentialsstochastic calculus of variation

Mathematics Subject Classification ID

Random fields (60G60) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic integral equations (60H20)

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A Gibson approach to infinite-dimensional Brownian diffusions ⋮ Stochastic dynamics for an infinite system of random closed strings: A Gibbsian point of view ⋮ Gaussian measures on linear spaces ⋮ Locally interacting diffusions as Markov random fields on path space ⋮ Ergodicity of \(L^ 2\)-semigroups and extremality of Gibbs states ⋮ A characterization of canonical Gibbs fields on \(\mathbb{R}^d\) and \(\mathcal C([0,1,\mathbb{R}^d)\)] ⋮ Differentiable measures and the Malliavin calculus ⋮ Duality formula for the bridges of a Brownian diffusion: Application to gradient drifts ⋮ Stochastic analysis on product manifolds: Dirichlet operators on differential forms

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