Diffusions in random environment and ballistic behavior
Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 6, pp. 683-714.
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Schmitz, Tom. Diffusions in random environment and ballistic behavior. Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 6, pp. 683-714. doi : 10.1016/j.anihpb.2005.08.003. http://archive.numdam.org/articles/10.1016/j.anihpb.2005.08.003/

[1] D.G. Aronson, Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa 22 (1968) 607-694. | EuDML | Numdam | MR | Zbl

[2] R. Bass, Diffusions and Elliptic Operators, Springer-Verlag, 1998. | MR | Zbl

[3] E. Bolthausen, A.-S. Sznitman, On the static and dynamic points of view for certain random walks in random environment, Methods Appl. Anal. 9 (3) (2002) 345-376. | MR | Zbl

[4] E. Bolthausen, A.-S. Sznitman, Ten Lectures on Random Media, DMV-Lectures, vol. 32, Birkhäuser, Basel, 2002. | MR | Zbl

[5] E. Bolthausen, A.-S. Sznitman, O. Zeitouni, Cut points and diffusive random walks in random environment, Ann. Inst. H. Poincaré Probab. Statist. 39 (3) (2003) 527-555. | EuDML | Numdam | MR | Zbl

[6] F. Comets, O. Zeitouni, A law of large numbers for random walks in random mixing environments, Ann. Probab. 32 (1B) (2004) 880-914. | MR | Zbl

[7] A. De Masi, P.A. Ferrari, S. Goldstein, W.D. Wick, An invariance principle for reversible Markov processes. Applications to random motions in random environments, J. Statist. Phys. 55 (1989) 787-855. | MR | Zbl

[8] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of the Second Order, Springer-Verlag, 1998. | Zbl

[9] A.M. Il'In, A.S. Kalashnikov, O.A. Oleinik, Linear equations of the second order of parabolic type, Russian Math. Surveys 17 (3) (1962) 1-143.

[10] S.A. Kalikow, Generalized random walk in a random environment, Ann. Probab. 9 (1981) 753-768. | MR | Zbl

[11] I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, 1991. | MR | Zbl

[12] C. Kipnis, S.R.S. Varadhan, A central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, Comm. Math. Phys. 104 (1986) 1-19. | MR | Zbl

[13] T. Komorowski, Stationarity of Lagrangian velocity in compressible environments, Comm. Math. Phys. 228 (3) (2002) 417-434. | MR | Zbl

[14] T. Komorowski, G. Krupa, On the existence of invariant measure for Lagrangian velocity in compressible environments, J. Statist. Phys. 106 (3-4) (2002) 635-651. | MR | Zbl

[15] T. Komorowski, G. Krupa, On stationarity of Lagrangian observations of passive tracer velocity in a compressible environment, Ann. Appl. Probab. 14 (4) (2004) 1666-1697. | MR | Zbl

[16] T. Komorowski, S. Olla, On homogenization of time-dependent random flows, Probab. Theory Related Fields 121 (1) (2001) 98-116. | MR | Zbl

[17] T. Komorowski, S. Olla, Invariant measures for passive tracer dynamics in Ornstein-Uhlenbeck flows, Stochastic Process Appl. 105 (2003) 139-173. | MR | Zbl

[18] S.M. Kozlov, The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys 40 (1985) 73-145. | MR | Zbl

[19] C. Landim, S. Olla, H.T. Yau, Convection-diffusion equation with space-time ergodic random flow, Probab. Theory Related Fields 112 (1998) 203-220. | MR | Zbl

[20] T.J. Lyons, W.A. Zheng, On conditional diffusion processes, Proc. Roy. Soc. Edinburgh Sect. A 115 (3-4) (1990) 243-255. | MR | Zbl

[21] S.A. Molchanov, Lectures on random media, in: Lecture Notes in Math., vol. 1581, Springer-Verlag, 1994, pp. 242-411. | MR | Zbl

[22] K. Oelschläger, Homogenization of a diffusion process in a divergence-free random field, Ann. Probab. 16 (3) (1988) 1084-1126. | MR | Zbl

[23] S. Olla, Homogenization of diffusion processes in random fields, Ecole Doctorale, Ecole Polytechnique, Palaiseau, 1994.

[24] S. Olla, Central limit theorems for tagged particles and for diffusions in random environment, in: Milieux Aléatoires, Panoramas et Synthèses, Numéro 12, Société Mathématique de France, 2001. | MR | Zbl

[25] G. Papanicolaou, S.R.S. Varadhan, Diffusion with random coefficients, in: Kallianpur G., Krishnajah P.R., Gosh J.K. (Eds.), Statistics and Probability: Essays in Honor of C.R. Rao, North-Holland, Amsterdam, 1982, pp. 547-552. | MR | Zbl

[26] F. Rassoul-Agha, The point of view of the particle on the law of large numbers for random walks in a mixing random environment, Ann. Probab. 31 (3) (2003) 1441-1463. | MR | Zbl

[27] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer-Verlag, Berlin, 1999. | MR | Zbl

[28] L. Shen, On ballistic diffusions in random environment, Ann. Inst. H. Poincaré Probab. Statist. 39 (5) (2003) 839-876. | Numdam | MR | Zbl

[29] L. Shen, Addendum to “On ballistic diffusions in random environment”, Ann. Inst. H. Poincaré Probab. Statist. 40 (3) (2004) 385-386. | Numdam | Zbl

[30] D. Stroock, Diffusion semigroups corresponding to uniformly elliptic divergence form operators, in: Lecture Notes in Math., vol. 1321, Springer-Verlag, Berlin, 1988, pp. 316-347. | Numdam | MR | Zbl

[31] A.-S. Sznitman, Slowdown estimates and central limit theorem for random walks in random environment, J. Eur. Math. Soc. 2 (2000) 93-143. | MR | Zbl

[32] A.-S. Sznitman, On a class of transient random walks in random environment, Ann. Probab. 29 (2) (2001) 723-764. | MR | Zbl

[33] A.-S. Sznitman, An effective criterion for ballistic behavior of random walks in random environment, Probab. Theory Related Fields 122 (4) (2002) 509-544. | MR | Zbl

[34] A.-S. Sznitman, On new examples of ballistic random walks in random environment, Ann. Probab. 31 (1) (2003) 285-322. | MR | Zbl

[35] A.-S. Sznitman, Topics in random walks in random environment, in: ICTP Lecture Notes Series, vol. XVII: School and Conference on Probability Theory, May 2004. | MR | Zbl

[36] A.-S. Sznitman, M.P.W. Zerner, A law of large numbers for random walks in random environment, Ann. Probab. 27 (4) (1999) 1851-1869. | MR | Zbl

[37] O. Zeitouni, Random Walks in Random Environment, in: Lecture Notes in Math., vol. 1837, Springer, 2004, pp. 190-312. | MR | Zbl

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