On ballistic diffusions in random environment
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 5, pp. 839-876.
corrigé par Addendum to the article “On ballistic diffusions in random environment” 
@article{AIHPB_2003__39_5_839_0,
     author = {Shen, Lian},
     title = {On ballistic diffusions in random environment},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {839--876},
     publisher = {Elsevier},
     volume = {39},
     number = {5},
     year = {2003},
     doi = {10.1016/S0246-0203(03)00027-X},
     mrnumber = {1997215},
     zbl = {1026.60096},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0246-0203(03)00027-X/}
}
TY  - JOUR
AU  - Shen, Lian
TI  - On ballistic diffusions in random environment
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2003
SP  - 839
EP  - 876
VL  - 39
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S0246-0203(03)00027-X/
DO  - 10.1016/S0246-0203(03)00027-X
LA  - en
ID  - AIHPB_2003__39_5_839_0
ER  - 
%0 Journal Article
%A Shen, Lian
%T On ballistic diffusions in random environment
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2003
%P 839-876
%V 39
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S0246-0203(03)00027-X/
%R 10.1016/S0246-0203(03)00027-X
%G en
%F AIHPB_2003__39_5_839_0
Shen, Lian. On ballistic diffusions in random environment. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 5, pp. 839-876. doi : 10.1016/S0246-0203(03)00027-X. http://www.numdam.org/articles/10.1016/S0246-0203(03)00027-X/

[1] R.J. Adler, The Geometry of Random Fields, Wiley, New York, 1981. | MR | Zbl

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

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

[4] F. Comets, O. Zeitouni, A law of large numbers for random walks in random mixing environments, preprint. | MR

[5] 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

[6] R. Durrett, Stochastic Calculus, CRC Press, Boca Raton, 1996. | MR | Zbl

[7] S.N. Ethier, T.G. Kurtz, Markov Processes, Wiley, New York, 1986. | MR | Zbl

[8] A. Friedman, Stochastic Differential Equations and Applications, Vol. 1, Academic Press, San Diego, 1975. | MR | Zbl

[9] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland, Amsterdam, 1980. | MR | Zbl

[10] M. Fukushima, D. Stroock, Reversibility of solutions to martingale problems, in: Probability, Statistical Mechanics, and Number Theory, Adv. Math. Suppl. Stud., 9, Academic Press, San Diego, 1986, pp. 107-123. | MR | Zbl

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

[12] V.V. Jikov, S.M. Kozlov, O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, 1994. | MR | Zbl

[13] 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

[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. | Zbl

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

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

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

[18] J.L. Lebowitz, H. Rost, The Einstein relation for the displacement of a test particle in a random environment, Stochastic Process. Appl. 54 (1994) 183-196. | MR | Zbl

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

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

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

[22] H. Osada, Homogenization of diffusion processes with random stationary coefficients, in: Lecture Notes in Math., Vol. 1021, Springer, Berlin, 1983, pp. 507-517. | MR | Zbl

[23] G. Papanicolaou, S.R.S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, in: Fritz J., Szasz D. (Eds.), Random Fields, Janyos Bolyai Ser., North-Holland, 1981. | MR | Zbl

[24] M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. I: Functional Analysis, Academic Press, San Diego, 1980. | MR | Zbl

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

[26] W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973. | MR | Zbl

[27] L. Shen, Asymptotic properties of certain anisotropic walks in random media, Ann. Appl. Probab. 12 (2) (2002) 477-510. | MR | Zbl

[28] D. Stroock, Probability Theory, An Analytic View, Cambridge University Press, 1993. | MR | Zbl

[29] 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

[30] K.T. Sturm, Analysis on local Dirichlet Spaces - II. Upper Gaussian estimates for the fundamental solutions of parabolic equations, Osaka J. Math. 32 (1995) 275-312. | Zbl

[31] A.-S. Sznitman, Brownian Motion, Obstacles and Random Media, Springer-Verlag, Berlin, 1998. | MR | Zbl

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

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

[34] 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

[35] 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

[36] O. Zeitouni, Lecture notes on random walks in random environment, St. Flour lecture notes, http://www.ee.technion.ac.il/~zeitouni/ps/notes1.ps.

Cité par Sources :