On the sector condition and homogenization of diffusions with a Gaussian drift

Journal of Functional Analysis

Volumn 197, Issue 1, 2003, Pages 179-211

  Komorowski, Tomasz ^a   Olla, Stefano ^b  

^a MARIA CURIE SK ODOWSKA UNIVERSITY   (Poland)

^b UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Gaussian random fields; Hermite polynomials; Homogenization; Invariance principle; Martingale

Indexed keywords

EID: 0037428623     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(02)00039-3     Document Type: Article

References (21)

1. R.J. Adler, An Introduction to Continuity Extrema and Related Topics for General Gaussian Processes, IMS Lecture Notes, Vol. 12, Inst. Math. Stat., Hayward, California, 1990.
2. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968.
3. S. Ethier, T. Kurtz, Markov Processes, Wiley, New York, 1986.
4. C.A. Fannjiang, T. Komorowski, A martingale approach to homogenization of unbounded random flows, Ann. Probab. 25 (1997) 1872-1894.
5. A. Fannjiang, T. Komorowski, Diffusions in long-range correlated Ornstein-Uhlenbeck flows, preprint, 2001, available at http://www.golem.umcs.lublin.pl/~komorow/flps.zip
6. A. Fannjiang, T. Komorowski, Diffusive and non-diffusive limits of transport in non-mixing flows with power-law spectra, SIAM J. Appl. Math. 62 (2002) 909-923.
7. A. Fannjiang, T. Komorowski, Sz. Peszat, Lagrangian dynamics for a passive tracer in a class of Gaussian Markovian flows, Stochastic Process. Appl. 97 (2002) 171-198.
8. S. Janson, Gaussian Hilbert Spaces, in: Cambridge Tracts in Mathematics, Vol. 129, Cambridge Univ. Press, Cambridge, 1997.
9. C. Kipnis, S.R.S. Varadhan, Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Comm. Math. Phys. 104 (1986) 1-19.
10. T. Komorowski, An abstract Lagrangian process related to convection-diffusion of a passive tracer in a Markovian flow, Bull. Pol. Acad. Sci. 48 (2000) 413-427.
11. C. Landim, S. Olla, S.R.S. Varadhan, Asymptotic behavior of a tagged particle in simple exclusion processes, Bol. Soc. Bras. Mat. 31 (2000) 241-275.
12. C. Landim, S. Olla, S.R.S. Varadhan, Symmetric simple exclusion process: regularity of the self-diffusion coefficient, Comm. Math. Phys. 224 (2001) 307-321.
13. K. Oelschläger, Homogenization of a diffusion process in a divergence free random field, Ann. Probab. 16 (1988) 1084-1126.
14. S. Olla, Notes on Central Limit Theorem for Tagged Particles and Diffusions in Random Environment, Notes of the Course given at Etáts de la Recherche: Mileaux Aléatoires CIRM, Luminy, pp. 23-25, November 2000, in: F. Comets, E. Pardoux (Eds.), Milieux Aléatoires, Panorama et Synthése, Available at http://www.cmap.polytechnique.fr/~olla/cirm.ps
15. H. Osada, T. Saitoh, An invariance principle for non-symmetric Markov processes and reflecting diffusions in random domains, Probab. Theory Related Fields 101 (1995) 45-63.
16. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
17. M. Reed, B. Simon, Methods of Modern Mathematical Physics II, Academic Press, New York, London.
18. Yu. A. Rozanov, Stationary Random Processes, Holden-Day, San Francisco, CA, 1969.
19. S. Sethuraman, S.R.S. Varadhan, H.T. Yau, Diffusive limit of a tagged particle in asymmetric simple exclusion process, Comm. Pure Appl. Math. 53 (2000) 972-1006.
20. S.R.S. Varadhan, Self diffusion of a tagged particle in equilibrium for asymmetric mean zero random walks with simple exclusion, Ann. Inst. Henri Poincare-Probab. Statist. 31 (1995) 273-285.
21. L. Wu, Forward-backward martingale decomposition and compactness results for additive functionals of stationary ergodic Markov processes, Ann. Inst. Henri Poincare-Probab. Statist. 35 (1999) 121-141.