@article{AIHPB_2007__43_1_101_0,
author = {Singh, Arvind},
title = {Limiting behavior of a diffusion in an asymptotically stable environment},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
volume = {43},
year = {2007},
pages = {101-138},
doi = {10.1016/j.anihpb.2006.01.003},
mrnumber = {2288272},
zbl = {1123.60075},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPB_2007__43_1_101_0}
}
Singh, Arvind. Limiting behavior of a diffusion in an asymptotically stable environment. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) pp. 101-138. doi : 10.1016/j.anihpb.2006.01.003. http://gdmltest.u-ga.fr/item/AIHPB_2007__43_1_101_0/
[1] , Lévy processes, Cambridge Tracts in Math., vol. 121, Cambridge University Press, Cambridge, 1996. | MR 1406564 | Zbl 0861.60003
[2] , 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
[3] , , On conditioning a random walk to stay nonnegative, Ann. Probab. 22 (4) (1994) 2152-2167. | MR 1331218 | Zbl 0834.60079
[4] , , , Regular Variation, Encyclopedia Math. Appl., vol. 27, Cambridge University Press, Cambridge, 1989. | MR 1015093 | Zbl 0667.26003
[5] , Large deviations probabilities for random walks in the absence of finite expectations of jumps, Probab. Theory Related Fields 125 (3) (2003) 421-446. | MR 1967023 | Zbl 1028.60021
[6] , A one-dimensional diffusion process in a Wiener medium, Ann. Probab. 14 (4) (1986) 1206-1218. | MR 866343 | Zbl 0608.60072
[7] , One-dimensional diffusion in an asymmetric random environment, Ann. Inst. H. Poincaré Probab. Statist., in press, available at, http://www.math.toronto.edu/dimitris. | Numdam | MR 2269235 | Zbl 1105.60077
[8] , Conditional limit theorems for asymptotically stable random walks, Z. Wahrsch. Verw. Gebiete 70 (3) (1985) 351-360. | MR 803677 | Zbl 0573.60063
[9] , On the law of the iterated logarithm, Ann. of Math. (2) 43 (1942) 419-436. | MR 6630 | Zbl 0063.01264
[10] , An Introduction to Probability Theory and its Applications, vol. II, John Wiley & Sons Inc., New York, 1966. | MR 210154 | Zbl 0138.10207
[11] , On large deviation probabilities in the case of attraction to a non-normal stable law, Sankhyā Ser. A 30 (1968) 253-258. | MR 240854 | Zbl 0182.22903
[12] , , The limits of Sinai's simple random walk in random environment, Ann. Probab. 26 (4) (1998) 1477-1521. | MR 1675031 | Zbl 0936.60088
[13] , , Diffusion Processes and their Sample Paths, Grundlehren Math. Wiss., Band 125, Academic Press Inc., New York, 1965. | MR 199891 | Zbl 0285.60063
[14] , , Limit Theorems for Stochastic Processes, Grundlehren Math. Wiss., vol. 288, Springer-Verlag, Berlin, 1987. | MR 959133 | Zbl 0635.60021
[15] , , , Localization of diffusion processes in one-dimensional random environment, J. Math. Soc. Japan 44 (3) (1992) 515-550. | MR 1167381 | Zbl 0761.60072
[16] , , A note on the Borel-Cantelli lemma, Illinois J. Math. 8 (1964) 248-251. | Zbl 0139.35401
[17] , 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
[18] , Distribution of the first ladder moment and height, and fluctuations of a random walk, Teor. Veroyatnost. i Primenen. 16 (1971) 539-613. | MR 290473 | Zbl 0269.60053
[19] , Diffusions with random coefficients, in: Particle Systems, Random Media and Large Deviations (Brunswick, Maine, 1984), Contemp. Math., vol. 41, Amer. Math. Soc., Providence, RI, 1985, pp. 351-356. | MR 814724 | Zbl 0572.60053
[20] , Sinai's walk via stochastic calculus, Survey paper, available at, http://www.proba.jussieu.fr/pageperso/zhan/preprints.html. | MR 2226845
[21] , Limit theorems for stochastic processes with independent increments, Teor. Veroyatnost. i Primenen. 2 (1957) 145-177. | MR 94842 | Zbl 0097.13001
[22] , One-Dimensional Stable Distributions, Transl. Math. Monogr., vol. 65, Amer. Math. Soc., Providence, RI, 1986, (Translated from the Russian by H.H. McFaden, translation edited by Ben Silver). | MR 854867 | Zbl 0589.60015