Diffusions in random environment and ballistic behavior

Tom Schmitz

Annales de l'I.H.P. Probabilités et statistiques (2006)

  • Volume: 42, Issue: 6, page 683-714
  • ISSN: 0246-0203

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Schmitz, Tom. "Diffusions in random environment and ballistic behavior." Annales de l'I.H.P. Probabilités et statistiques 42.6 (2006): 683-714. <http://eudml.org/doc/77915>.

@article{Schmitz2006,
author = {Schmitz, Tom},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {condition },
language = {eng},
number = {6},
pages = {683-714},
publisher = {Elsevier},
title = {Diffusions in random environment and ballistic behavior},
url = {http://eudml.org/doc/77915},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Schmitz, Tom
TI - Diffusions in random environment and ballistic behavior
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2006
PB - Elsevier
VL - 42
IS - 6
SP - 683
EP - 714
LA - eng
KW - condition
UR - http://eudml.org/doc/77915
ER -

References

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  1. [1] D.G. Aronson, Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa22 (1968) 607-694. Zbl0182.13802MR435594
  2. [2] R. Bass, Diffusions and Elliptic Operators, Springer-Verlag, 1998. Zbl0914.60009MR1483890
  3. [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. Zbl1079.60079MR2023130
  4. [4] E. Bolthausen, A.-S. Sznitman, Ten Lectures on Random Media, DMV-Lectures, vol. 32, Birkhäuser, Basel, 2002. Zbl1075.60128MR1890289
  5. [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. Zbl1016.60094MR1978990
  6. [6] F. Comets, O. Zeitouni, A law of large numbers for random walks in random mixing environments, Ann. Probab.32 (1B) (2004) 880-914. Zbl1078.60089MR2039946
  7. [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. Zbl0713.60041MR1003538
  8. [8] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of the Second Order, Springer-Verlag, 1998. Zbl1042.35002
  9. [9] A.M. Il'in, A.S. Kalashnikov, O.A. Oleinik, Linear equations of the second order of parabolic type, Russian Math. Surveys17 (3) (1962) 1-143. 
  10. [10] S.A. Kalikow, Generalized random walk in a random environment, Ann. Probab.9 (1981) 753-768. Zbl0545.60065MR628871
  11. [11] I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag, 1991. Zbl0734.60060MR1121940
  12. [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. Zbl0588.60058MR834478
  13. [13] T. Komorowski, Stationarity of Lagrangian velocity in compressible environments, Comm. Math. Phys.228 (3) (2002) 417-434. Zbl1009.76036MR1918783
  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. Zbl0996.60065MR1884548
  15. [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. Zbl1075.60021MR2099648
  16. [16] T. Komorowski, S. Olla, On homogenization of time-dependent random flows, Probab. Theory Related Fields121 (1) (2001) 98-116. Zbl0996.60040MR1857110
  17. [17] T. Komorowski, S. Olla, Invariant measures for passive tracer dynamics in Ornstein–Uhlenbeck flows, Stochastic Process Appl.105 (2003) 139-173. Zbl1075.76550MR1972292
  18. [18] S.M. Kozlov, The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys40 (1985) 73-145. Zbl0615.60063MR786087
  19. [19] C. Landim, S. Olla, H.T. Yau, Convection–diffusion equation with space–time ergodic random flow, Probab. Theory Related Fields112 (1998) 203-220. Zbl0914.60070MR1653837
  20. [20] T.J. Lyons, W.A. Zheng, On conditional diffusion processes, Proc. Roy. Soc. Edinburgh Sect. A115 (3–4) (1990) 243-255. Zbl0715.60097MR1069520
  21. [21] S.A. Molchanov, Lectures on random media, in: Lecture Notes in Math., vol. 1581, Springer-Verlag, 1994, pp. 242-411. Zbl0814.60093MR1307415
  22. [22] K. Oelschläger, Homogenization of a diffusion process in a divergence-free random field, Ann. Probab.16 (3) (1988) 1084-1126. Zbl0653.60047MR942757
  23. [23] S. Olla, Homogenization of diffusion processes in random fields, Ecole Doctorale, Ecole Polytechnique, Palaiseau, 1994. 
  24. [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. Zbl1119.60302MR2226846
  25. [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. Zbl0486.60076MR659505
  26. [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. Zbl1039.60089MR1989439
  27. [27] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer-Verlag, Berlin, 1999. Zbl0731.60002MR1725357
  28. [28] L. Shen, On ballistic diffusions in random environment, Ann. Inst. H. Poincaré Probab. Statist.39 (5) (2003) 839-876. Zbl1026.60096MR1997215
  29. [29] L. Shen, Addendum to “On ballistic diffusions in random environment”, Ann. Inst. H. Poincaré Probab. Statist.40 (3) (2004) 385-386. Zbl1043.60067
  30. [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. Zbl0651.47031MR960535
  31. [31] A.-S. Sznitman, Slowdown estimates and central limit theorem for random walks in random environment, J. Eur. Math. Soc.2 (2000) 93-143. Zbl0976.60097MR1763302
  32. [32] A.-S. Sznitman, On a class of transient random walks in random environment, Ann. Probab.29 (2) (2001) 723-764. Zbl1017.60106MR1849176
  33. [33] 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
  34. [34] A.-S. Sznitman, On new examples of ballistic random walks in random environment, Ann. Probab.31 (1) (2003) 285-322. Zbl1017.60104MR1959794
  35. [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. Zbl1060.60102MR2198849
  36. [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. Zbl0965.60100MR1742891
  37. [37] O. Zeitouni, Random Walks in Random Environment, in: Lecture Notes in Math., vol. 1837, Springer, 2004, pp. 190-312. Zbl1060.60103MR2071631

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