One-dimensional diffusion in an asymmetric random environment
Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 6, p. 715-726
@article{AIHPB_2006__42_6_715_0,
     author = {Cheliotis, Dimitrios},
     title = {One-dimensional diffusion in an asymmetric random environment},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {42},
     number = {6},
     year = {2006},
     pages = {715-726},
     doi = {10.1016/j.anihpb.2005.08.004},
     zbl = {1105.60077},
     mrnumber = {2269235},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2006__42_6_715_0}
}
Cheliotis, Dimitrios. One-dimensional diffusion in an asymmetric random environment. Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 6, pp. 715-726. doi : 10.1016/j.anihpb.2005.08.004. http://www.numdam.org/item/AIHPB_2006__42_6_715_0/

[1] F. Avram, A. Kyprianou, M. Pistorius, Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options, Ann. Appl. Probab. 14 (1) (2004) 215-238. | MR 2023021 | Zbl 1042.60023

[2] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1996. | MR 1406564 | Zbl 0861.60003

[3] J. Bertoin, On the first exit time of a completely asymmetric stable process from a finite interval, Bull. London Math. Soc. 28 (5) (1996) 514-520. | MR 1396154 | Zbl 0863.60068

[4] J. Bertoin, Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval, Ann. Appl. Probab. 7 (1997) 156-169. | MR 1428754 | Zbl 0880.60077

[5] T. Brox, A one-dimensional diffusion process in a Wiener medium, Ann. Probab. 14 (4) (1986) 1206-1218. | MR 866343 | Zbl 0608.60072

[6] R. Durrett, Probability: Theory and Examples, Wadsworth Pub. Co., 1996. | MR 1609153 | Zbl 0709.60002

[7] A. Erdélyi, W. Magnus, F. Oberhettinger, F. Tricomi, Higher Transcendental Functions, vol. 1, McGraw-Hill Book Company, Inc., New York, 1953, Based, in part, on notes left by Harry Bateman. | MR 58756 | Zbl 0051.30303

[8] A.O. Golosov, Limit distributions for random walks in random environments, Soviet Math. Dokl. 28 (1983) 18-22.

[9] P. Greenwood, J. Pitman, Fluctuation identities for Lévy processes and splitting at the maximum, Adv. Appl. Probab. 12 (1980) 893-902. | MR 588409 | Zbl 0443.60037

[10] H. Kesten, The limit distribution of Sinai's random walk in random environment, Phys. A 138 (1-2) (1986) 299-309. | MR 865247 | Zbl 0666.60065

[11] M. Pistorius, On exit and ergodicity of the spectrally one-sided Lévy process reflected at its infimum, J. Theoret. Probab. 17 (1) (2004) 183-220. | MR 2054585 | Zbl 1049.60042

[12] L.C.G. Rogers, D. Williams, Diffusions, Markov Processes, and Martingales, vol. 2, John Wiley and Sons, Inc., New York, 1987. | MR 921238 | Zbl 0627.60001

[13] S. Schumacher, Diffusions with random coefficients, in: Particle Systems, Random Media and Large Deviations, Contemp. Math., vol. 41, Amer. Math. Soc., Providence, RI, 1985. | MR 814724 | Zbl 0572.60053

[14] S. Schumacher, Diffusions with Random Coefficients, Ph.D. thesis, UCLA, 1984. | MR 814724 | Zbl 0572.60053

[15] P. Seignourel, Discrete schemes for processes in random media, Probab. Theory Related Fields 118 (3) (2000) 293-322. | MR 1800534 | Zbl 0968.60100

[16] Z. Shi, Sinai's walk via stochastic calculus, in: Comets F., Pardoux E. (Eds.), Milieux Aléatoires, Panoramas et Synthèses, vol. 12, Société Mathématique de France, 2001. | MR 2238823 | Zbl 1031.60088

[17] Y. Sinai, The limiting behavior of a one-dimensional random walk in a random medium, Theory Probab. Appl. 27 (1982) 256-268. | MR 657919 | Zbl 0505.60086

[18] H. Tanaka, Limit distributions for one-dimensional diffusion processes in self-similar random environments, in: Hydrodynamic Behavior and Interacting Particle Systems, IMA Vol. Math. Appl., vol. 9, Springer, 1987, pp. 189-210. | MR 914995 | Zbl 0653.60072

[19] H. Tanaka, Limit distribution for 1-dimensional diffusion in a reflected Brownian medium, in: Séminaire de Probabilités, XXI, Lecture Notes in Math., vol. 1247, Springer, 1987, pp. 246-261. | Numdam | MR 941988 | Zbl 0616.60074