Small perturbation of diffusions in inhomogeneous media
Chiang, Tzuu-Shuh ; Sheu, Shuenn-Jyi
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002), p. 285-318 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2002-01-01
@article{AIHPB_2002__38_3_285_0,
     author = {Chiang, Tzuu-Shuh and Sheu, Shuenn-Jyi},
     title = {Small perturbation of diffusions in inhomogeneous media},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {38},
     year = {2002},
     pages = {285-318},
     mrnumber = {1899455},
     zbl = {1002.60070},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2002__38_3_285_0}
}

Chiang, Tzuu-Shuh; Sheu, Shuenn-Jyi. Small perturbation of diffusions in inhomogeneous media. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) pp. 285-318. http://gdmltest.u-ga.fr/item/AIHPB_2002__38_3_285_0/

[1] M. Alanyali, B. Hajek, On large deviations of Markov processes with discontinuous statistics, Ann. Appl. Probab. 8 (1998) 45-66. | MR 1620409 | Zbl 0936.60021

[2] M. Alanyali, B. Hajek, On large deviations in load sharing network, Ann. Appl. Probab. 8 (1998) 67-97. | MR 1620334 | Zbl 0938.60097

[3] R. Azencott, Probabilités de Saint-Flour VIII, in: Lecture Notes in Mathematics, 774, 1980, pp. 1-176. | MR 590626 | Zbl 0435.60028

[4] R. Azencott, G. Ruget, Melanges d'équations differentialles et grands écarts à la loi des grand nombres, Z. Wahrsch. Verw. Gebiete 38 (1977) 1-54. | MR 443097 | Zbl 0372.60082

[5] V.M. Blinovskii, R.L. Dobrushin, Process level large deviations for a class of piecewise homogeneous random walks, in: The Dynkin Festschrift: Markov Processes and Their Applications, 1994, pp. 1-59. | MR 1311710 | Zbl 0819.60029

[6] M. Boué, P. Dupuis, R. Ellis, Large deviations for diffusions with discontinuous statistics, Probab. Theory Related Fields 116 (2000) 125-149. | MR 1736592 | Zbl 0949.60046

[7] T.S. Chiang, S.J. Sheu, Large deviations of small perturbation of some unstable systems, Stochastic Anal. Appl. 15 (1997) 31-50. | MR 1429856 | Zbl 0873.60013

[8] T.S. Chiang, S.J. Sheu, Large deviations of diffusion processes with discontinuous drift and their occupation times, Ann. Probab. 28 (2000) 140-165. | MR 1756001 | Zbl 1044.60065

[9] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Jones and Bartlett, 1992. | MR 1202429 | Zbl 0793.60030

[10] P. Dupuis, R. Ellis, Large deviations for Markov process with discontinuous statistics. II: Random walks, Probab. Theory Related Fields 91 (1992) 153-194. | MR 1147614 | Zbl 0746.60025

[11] P. Dupuis, R. Ellis, The large deviation principle for a general class of queueing systems I, Trans. AMS 347 (1995) 2689-2751. | MR 1290716 | Zbl 0869.60022

[12] P. Dupuis, R. Ellis, A Weak Convergence Approach to the Theory of Large Deviations, Wiley, 1997. | MR 1431744 | Zbl 0904.60001

[13] M. Freidlin, S.J. Sheu, Diffusion processes on graphs: stochastic differential equations, large deviation principle, Probab. Theory Related Fields 116 (2000) 181-220. | MR 1743769 | Zbl 0957.60088

[14] M.I. Freidlin, A.D. Wentzell, Random Perturbations of Dynamical Systems, Springer-Verlag, 1984. | MR 722136 | Zbl 0922.60006

[15] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, 1981. | MR 1011252 | Zbl 0684.60040

[16] A.P. Korostelev, S.L. Leonov, Actional functional for diffusion process with discontinuous drift, Theory Probab. Appl. 37 (1992) 543-550. | MR 1214364 | Zbl 0788.60094

[17] A.P. Korostelev, S.L. Leonov, Actional functional for diffusions in discontinuous media, Probab. Theory Related Fields 94 (1992) 317-333. | MR 1198651 | Zbl 0767.60023

[18] I. Nagot, Grandes déviations pour les processus d'apprentissages lent à statistiques discontinues sur une surface, Thèse de Docteur en Sciences, Université Paris XI Orsay, U.F.R. Scientique d'Orsay, 1995.

[19] G. Pinsky Ross, Positive Harmonic Functions and Diffusion, Cambridge Studies in Advanced Mathematics, 45, 1995. | MR 1326606 | Zbl 0858.31001

[20] M. Schilder, Some asymptotic formulae for Wiener integrals, Trans. Amer. Math. Soc. 125 (1966) 63-85. | MR 201892 | Zbl 0156.37602

[21] S. Varadhan, Lectures on Diffusion Problems and Partial Differential Equations, TATA Institute of Fundament Research, Bombay, 1980. | MR 607678 | Zbl 0489.35002

[22] S. Varadhan, Large Deviations and Applications, Society for Industrial and Applied Mathematics, Philadelphia, 1984. | MR 758258

[23] M. Yor, Sur la continuité des temps locaux associés à certaines semi-martingales, in: Astérique, 52-53, Société Mathématique de France, 1978, pp. 23-35.