One-dimensional diffusion in an asymmetric random environment

 Access to full text

 Full (PDF)

1. [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. Zbl1042.60023MR2023021
2. [2] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1996. Zbl0861.60003MR1406564
3. [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. Zbl0863.60068MR1396154
4. [4] J. Bertoin, Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval, Ann. Appl. Probab.7 (1997) 156-169. Zbl0880.60077MR1428754
5. [5] T. Brox, A one-dimensional diffusion process in a Wiener medium, Ann. Probab.14 (4) (1986) 1206-1218. Zbl0608.60072MR866343
6. [6] R. Durrett, Probability: Theory and Examples, Wadsworth Pub. Co., 1996. Zbl0709.60002MR1609153
7. [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. Zbl0051.30303MR58756
8. [8] A.O. Golosov, Limit distributions for random walks in random environments, Soviet Math. Dokl.28 (1983) 18-22. 
9. [9] P. Greenwood, J. Pitman, Fluctuation identities for Lévy processes and splitting at the maximum, Adv. Appl. Probab.12 (1980) 893-902. Zbl0443.60037MR588409
10. [10] H. Kesten, The limit distribution of Sinai's random walk in random environment, Phys. A138 (1–2) (1986) 299-309. Zbl0666.60065MR865247
11. [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. Zbl1049.60042MR2054585
12. [12] L.C.G. Rogers, D. Williams, Diffusions, Markov Processes, and Martingales, vol. 2, John Wiley and Sons, Inc., New York, 1987. Zbl0627.60001MR921238
13. [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. Zbl0572.60053MR814724
14. [14] S. Schumacher, Diffusions with Random Coefficients, Ph.D. thesis, UCLA, 1984. Zbl0572.60053MR814724
15. [15] P. Seignourel, Discrete schemes for processes in random media, Probab. Theory Related Fields118 (3) (2000) 293-322. Zbl0968.60100MR1800534
16. [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. Zbl1031.60088MR2238823
17. [17] Y. Sinai, The limiting behavior of a one-dimensional random walk in a random medium, Theory Probab. Appl.27 (1982) 256-268. Zbl0505.60086MR657919
18. [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. Zbl0653.60072MR914995
19. [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. Zbl0616.60074MR941988

1. Arvind Singh, Limiting behavior of a diffusion in an asymptotically stable environment