Homogenization with respect to Gibbs measures for periodic drift diffusions on lattices
Sergio A Albeverio, Maria Simonetta Bernabei, Michael Röckner, Minoru W. Yoshida · Comptes Rendus Mathématique · 2005
A homogenization problem for infinite dimensional diffusion processes indexed by Z d having periodic drift coefficients is considered. By an application of the uniform ergodic theorem for the infinite dimensional diffusion processes based on logarithmic Sobolev inequalities, an L 1 type homogenization property of the processes with respect to an invariant measure is proved. This is the, so far, best possible analogue in infinite dimensions to a known result in the finite dimensional case (cf. [G. Papanicolaou, S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, Seria Coll. Math. Soc. Janos Bolyai, vol. 27, North-Holland, 1979. [4]]).