On the existence of an invariant measure for isotropic diffusions in random environment

被引：1

作者：

Fehrman, Benjamin J. ^{[1
]}

机构：

[1] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2017年 / 168卷 / 1-2期

关键词：

Invariant measure; Stochastic homogenization; Diffusion in random environment; PRINCIPLE;

D O I：

10.1007/s00440-016-0714-4

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The results of this paper build upon those first obtained by Sznitman and Zeitouni (Invent Math 164(3), 455-567, 2006). We establish, for spacial dimensions , the existence of a unique invariant measure for isotropic diffusions in random environment on which are small perturbations of Brownian motion. Furthermore, we establish a general homogenization result for initial data which are locally measurable with respect to the coefficients.

引用

页码：409 / 453

页数：45

共 13 条

[1]

[Anonymous], 2006, Classics in Mathematics

[2]

[Anonymous], 2011, ASYMPTOTIC ANAL PERI, DOI DOI 10.1090/CHEL/374

[3] RANDOM-WALKS IN ASYMMETRIC RANDOM-ENVIRONMENTS [J].

BRICMONT, J ;

KUPIAINEN, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1991, 142 (02) :345-420

[4] AN INVARIANCE-PRINCIPLE FOR REVERSIBLE MARKOV-PROCESSES - APPLICATIONS TO RANDOM MOTIONS IN RANDOM-ENVIRONMENTS [J].

DEMASI, A ;

FERRARI, PA ;

GOLDSTEIN, S ;

WICK, WD .

JOURNAL OF STATISTICAL PHYSICS, 1989, 55 (3-4) :787-855

[5]

FRIEDMAN A., 1964, Partial differential equations of parabolic type

[6]

Kozlov S. M., 1985, USP MAT NAUK, V40, p[61, 238]

[7]

OLLA S, 1994, HOMOGENIZATION DIFFU

[8]

OSADA H, 1983, LECT NOTES MATH, V1021, P507

[9]

Papanicolaou G., 1982, Statistics and Probability, P547

[10]

Papanicolaou GC., 1979, Colloquia mathematica Societatis Jnos Bolyai, V27, P835

← 1 2 →