Small perturbation of diffusions in inhomogeneous media

 Access to full text

 Full (PDF)

1. [1] M. Alanyali, B. Hajek, On large deviations of Markov processes with discontinuous statistics, Ann. Appl. Probab.8 (1998) 45-66. Zbl0936.60021MR1620409
2. [2] M. Alanyali, B. Hajek, On large deviations in load sharing network, Ann. Appl. Probab.8 (1998) 67-97. Zbl0938.60097MR1620334
3. [3] R. Azencott, Probabilités de Saint-Flour VIII, in: Lecture Notes in Mathematics, 774, 1980, pp. 1-176. Zbl0435.60028MR590626
4. [4] R. Azencott, G. Ruget, Melanges d'équations differentialles et grands écarts à la loi des grand nombres, Z. Wahrsch. Verw. Gebiete38 (1977) 1-54. Zbl0372.60082MR443097
5. [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. Zbl0819.60029MR1311710
6. [6] M. Boué, P. Dupuis, R. Ellis, Large deviations for diffusions with discontinuous statistics, Probab. Theory Related Fields116 (2000) 125-149. Zbl0949.60046MR1736592
7. [7] T.S. Chiang, S.J. Sheu, Large deviations of small perturbation of some unstable systems, Stochastic Anal. Appl.15 (1997) 31-50. Zbl0873.60013MR1429856
8. [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. Zbl1044.60065MR1756001
9. [9] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Jones and Bartlett, 1992. Zbl0793.60030MR1202429
10. [10] P. Dupuis, R. Ellis, Large deviations for Markov process with discontinuous statistics. II: Random walks, Probab. Theory Related Fields91 (1992) 153-194. Zbl0746.60025MR1147614
11. [11] P. Dupuis, R. Ellis, The large deviation principle for a general class of queueing systems I, Trans. AMS347 (1995) 2689-2751. Zbl0869.60022MR1290716
12. [12] P. Dupuis, R. Ellis, A Weak Convergence Approach to the Theory of Large Deviations, Wiley, 1997. Zbl0904.60001MR1431744
13. [13] M. Freidlin, S.J. Sheu, Diffusion processes on graphs: stochastic differential equations, large deviation principle, Probab. Theory Related Fields116 (2000) 181-220. Zbl0957.60088MR1743769
14. [14] M.I. Freidlin, A.D. Wentzell, Random Perturbations of Dynamical Systems, Springer-Verlag, 1984. Zbl0922.60006MR722136
15. [15] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, 1981. Zbl0684.60040MR1011252
16. [16] A.P. Korostelev, S.L. Leonov, Actional functional for diffusion process with discontinuous drift, Theory Probab. Appl.37 (1992) 543-550. Zbl0788.60094MR1214364
17. [17] A.P. Korostelev, S.L. Leonov, Actional functional for diffusions in discontinuous media, Probab. Theory Related Fields94 (1992) 317-333. Zbl0767.60023MR1198651
18. [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. [19] G. Pinsky Ross, Positive Harmonic Functions and Diffusion, Cambridge Studies in Advanced Mathematics, 45, 1995. Zbl0858.31001MR1326606
20. [20] M. Schilder, Some asymptotic formulae for Wiener integrals, Trans. Amer. Math. Soc.125 (1966) 63-85. Zbl0156.37602MR201892
21. [21] S. Varadhan, Lectures on Diffusion Problems and Partial Differential Equations, TATA Institute of Fundament Research, Bombay, 1980. Zbl0489.35002MR607678
22. [22] S. Varadhan, Large Deviations and Applications, Society for Industrial and Applied Mathematics, Philadelphia, 1984. MR758258
23. [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.