One-dimensional diffusion in an asymmetric random environment
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 6, pp. 715-726. 
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     title = {One-dimensional diffusion in an asymmetric random environment},
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Cheliotis, Dimitrios. One-dimensional diffusion in an asymmetric random environment. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 6, pp. 715-726. doi : 10.1016/j.anihpb.2005.08.004. http://www.numdam.org/articles/10.1016/j.anihpb.2005.08.004/

[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 | Zbl

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

[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 | Zbl

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

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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

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

[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 | Zbl

[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. | EuDML | Numdam | MR | Zbl

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