On ballistic diffusions in random environment

 Access to full text

 Full (PDF)

1. [1] R.J. Adler, The Geometry of Random Fields, Wiley, New York, 1981. Zbl0478.60059MR611857
2. [2] R. Bass, Diffusions and Elliptic Operators, Springer-Verlag, Berlin, 1998. Zbl0914.60009MR1483890
3. [3] E. Bolthausen, A.-S. Sznitman, Ten Lectures on Random Media, DMV-Lectures, 32, Birkhäuser, Basel, 2002. Zbl1075.60128MR1890289
4. [4] F. Comets, O. Zeitouni, A law of large numbers for random walks in random mixing environments, preprint. Zbl1078.60089MR2039946
5. [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. Zbl0713.60041MR1003538
6. [6] R. Durrett, Stochastic Calculus, CRC Press, Boca Raton, 1996. Zbl0856.60002MR1398879
7. [7] S.N. Ethier, T.G. Kurtz, Markov Processes, Wiley, New York, 1986. Zbl0592.60049MR838085
8. [8] A. Friedman, Stochastic Differential Equations and Applications, Vol. 1, Academic Press, San Diego, 1975. Zbl0323.60056MR494490
9. [9] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland, Amsterdam, 1980. Zbl0422.31007MR569058
10. [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. Zbl0613.60066MR875449
11. [11] A.M. Il'in, A.S. Kalashnikov, O.A. Oleinik, Linear equations of the second order of parabolic type, Russian Math. Surveys17 (1) (1962) 1-143. 
12. [12] V.V. Jikov, S.M. Kozlov, O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, 1994. Zbl0838.35001MR1329546
13. [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. Zbl0588.60058MR834478
14. [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. Zbl0996.60065
15. [15] T. Komorowski, S. Olla, On homogenization of time-dependent random flows, Probab. Theory Related Fields121 (1) (2001) 98-116. Zbl0996.60040MR1857110
16. [16] S.M. Kozlov, The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys40 (1985) 73-145. Zbl0615.60063MR786087
17. [17] C. Landim, S. Olla, H.T. Yau, Convection-diffusion equation with space–time ergodic random flow, Probab. Theory Related Fields112 (1998) 203-220. Zbl0914.60070
18. [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. Zbl0812.60096MR1307334
19. [19] S.A. Molchanov, Lectures on random media, in: Lecture Notes in Math., Vol. 1581, Springer, Berlin, 1994, pp. 242-411. Zbl0814.60093MR1307415
20. [20] K. Oelschläger, Homogenization of a diffusion process in a divergence-free random fields, Ann. Probab.16 (3) (1988) 1084-1126. Zbl0653.60047MR942757
21. [21] S. Olla, Homogenization of diffusion processes in random fields, École Doctorale, École Polytechnique, Palaiseau, 1994. 
22. [22] H. Osada, Homogenization of diffusion processes with random stationary coefficients, in: Lecture Notes in Math., Vol. 1021, Springer, Berlin, 1983, pp. 507-517. Zbl0535.60071MR736016
23. [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. Zbl0499.60059MR712714
24. [24] M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. I: Functional Analysis, Academic Press, San Diego, 1980. Zbl0242.46001MR751959
25. [25] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer-Verlag, Berlin, 1999. Zbl0731.60002MR1725357
26. [26] W. Rudin, Functional Analysis, McGraw-Hill, New York, 1973. Zbl0253.46001MR365062
27. [27] L. Shen, Asymptotic properties of certain anisotropic walks in random media, Ann. Appl. Probab.12 (2) (2002) 477-510. Zbl1016.60092MR1910636
28. [28] D. Stroock, Probability Theory, An Analytic View, Cambridge University Press, 1993. Zbl0925.60004MR1267569
29. [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. Zbl0651.47031MR960535
30. [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. Zbl0854.35015
31. [31] A.-S. Sznitman, Brownian Motion, Obstacles and Random Media, Springer-Verlag, Berlin, 1998. Zbl0973.60003MR1717054
32. [32] A.-S. Sznitman, Slowdown estimates and central limit theorem for random walks in random environment, J. European Math. Soc.2 (2000) 93-143. Zbl0976.60097MR1763302
33. [33] A.-S. Sznitman, On a class of transient random walks in random environment, Ann. Probab.29 (2) (2001) 723-764. Zbl1017.60106MR1849176
34. [34] A.-S. Sznitman, An effective criterion for ballistic behavior of random walks in random environment, Probab. Theory Related Fields122 (4) (2002) 509-544. Zbl0995.60097MR1902189
35. [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. Zbl0965.60100MR1742891
36. [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. 

1. Lian Shen, Addendum to the article “On ballistic diffusions in random environment”
2. Tom Schmitz, Diffusions in random environment and ballistic behavior