@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] The Geometry of Random Fields, Wiley, New York, 1981. | MR | Zbl
,[2] Diffusions and Elliptic Operators, Springer-Verlag, Berlin, 1998. | MR | Zbl
,[3] 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] An invariance principle for reversible Markov processes. Applications to random motions in random environments, J. Statist. Phys. 55 (1989) 787-855. | MR | Zbl
, , , ,[6] Stochastic Calculus, CRC Press, Boca Raton, 1996. | MR | Zbl
,[7] Markov Processes, Wiley, New York, 1986. | MR | Zbl
, ,[8] Stochastic Differential Equations and Applications, Vol. 1, Academic Press, San Diego, 1975. | MR | Zbl
,[9] Dirichlet Forms and Markov Processes, North-Holland, Amsterdam, 1980. | MR | Zbl
,[10] 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] Linear equations of the second order of parabolic type, Russian Math. Surveys 17 (1) (1962) 1-143.
, , ,[12] Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, 1994. | MR | Zbl
, , ,[13] 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] On the existence of invariant measure for Lagrangian velocity in compressible environments, J. Statist. Phys. 106 (3-4) (2002) 635-651. | Zbl
, ,[15] On homogenization of time-dependent random flows, Probab. Theory Related Fields 121 (1) (2001) 98-116. | MR | Zbl
, ,[16] The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys 40 (1985) 73-145. | MR | Zbl
,[17] Convection-diffusion equation with space-time ergodic random flow, Probab. Theory Related Fields 112 (1998) 203-220. | Zbl
, , ,[18] The Einstein relation for the displacement of a test particle in a random environment, Stochastic Process. Appl. 54 (1994) 183-196. | MR | Zbl
, ,[19] Lectures on random media, in: Lecture Notes in Math., Vol. 1581, Springer, Berlin, 1994, pp. 242-411. | MR | Zbl
,[20] 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] Homogenization of diffusion processes with random stationary coefficients, in: Lecture Notes in Math., Vol. 1021, Springer, Berlin, 1983, pp. 507-517. | MR | Zbl
,[23] Boundary value problems with rapidly oscillating random coefficients, in: , (Eds.), Random Fields, Janyos Bolyai Ser., North-Holland, 1981. | MR | Zbl
, ,[24] Methods of Modern Mathematical Physics, Vol. I: Functional Analysis, Academic Press, San Diego, 1980. | MR | Zbl
, ,[25] Continuous Martingales and Brownian Motion, Springer-Verlag, Berlin, 1999. | MR | Zbl
, ,[26] Functional Analysis, McGraw-Hill, New York, 1973. | MR | Zbl
,[27] Asymptotic properties of certain anisotropic walks in random media, Ann. Appl. Probab. 12 (2) (2002) 477-510. | MR | Zbl
,[28] Probability Theory, An Analytic View, Cambridge University Press, 1993. | MR | Zbl
,[29] 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] 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] Brownian Motion, Obstacles and Random Media, Springer-Verlag, Berlin, 1998. | MR | Zbl
,[32] Slowdown estimates and central limit theorem for random walks in random environment, J. European Math. Soc. 2 (2000) 93-143. | MR | Zbl
,[33] On a class of transient random walks in random environment, Ann. Probab. 29 (2) (2001) 723-764. | MR | Zbl
,[34] 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 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.
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