Estimates in probability of the residual between the random and the homogenized solutions of one‐dimensional second‐order operator

Article type: Research Article

Authors: Bourgeat, A. | Piatnitski, A.

Affiliations: Université Jean Monnet, 23 rue du Dr. P. Michelon, 42023 Saint‐Etienne Cedex 02, France | P.N. Lebedev Physical Institute, Russian Academy of Sciences, Leninsky pr. 53, Moscow 117924, Russia

Abstract: The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one‐dimensional second‐order elliptic operators with random coefficients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coefficient.

Keywords: Stochastic homogenization, random operators, moderate deviations

Journal: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 303-315, 1999