Annealed deviations of random walk in random scenery

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1. [1] A. Asselah, F. Castell, Large deviations for Brownian motion in a random scenery, Probab. Theory Related Fields126 (2003) 497-527. Zbl1043.60018MR2001196
2. [2] A. Asselah, F. Castell, A note on random walk in random scenery, preprint, 2005. Zbl1112.60088
3. [3] A. Asselah, F. Castell, Self-intersection times for random walk, and random walk in random scenery in dimension $d\ge 5$, preprint, 2005. Zbl1116.60057
4. [4] G. Ben Arous, R. Léandre, Décroissance exponentielle du noyau de la chaleur sur la diagonale. II, Probab. Theory Related Fields90 (3) (1991) 377-402. Zbl0734.60027MR1133372
5. [5] N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987. Zbl0617.26001MR898871
6. [6] E. Bolthausen, A central limit theorem for two-dimensional random walks in random sceneries, Ann. Probab.17 (1989) 108-115. Zbl0679.60028MR972774
7. [7] A.N. Borodin, Limit theorems for sums of independent random variables defined on a transient random walk, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)85 (1979) 17-29, 237, 244. Zbl0417.60027MR535455
8. [8] A.N. Borodin, A limit theorem for sums of independent random variables defined on a recurrent random walk, Dokl. Akad. Nauk SSSR246 (4) (1979) 786-787. Zbl0423.60025MR543530
9. [9] D.C. Brydges, G. Slade, The diffusive phase of a model of self-interacting walks, Probab. Theory Related Fields103 (1995) 285-315. Zbl0832.60096MR1358079
10. [10] F. Castell, Moderate deviations for diffusions in a random Gaussian shear flow drift, Ann. Inst. H. Poincaré Probab. Statist.40 (3) (2004) 337-366. Zbl1042.60009MR2060457
11. [11] F. Castell, F. Pradeilles, Annealed large deviations for diffusions in a random shear flow drift, Stochastic Process Appl.94 (2001) 171-197. Zbl1051.60028MR1840830
12. [12] X. Chen, Exponential asymptotics and law of the iterated logarithm for intersection local times of random walks, Ann. Probab.32 (4) (2004). Zbl1067.60071MR2094445
13. [13] X. Chen, W. Li, Large and moderate deviations for intersection local times, Probab. Theory Related Fields128 (2004) 213-254. Zbl1038.60074MR2031226
14. [14] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, second ed., Springer, Berlin, 1998. Zbl0896.60013MR1619036
15. [15] M. Donsker, S.R.S. Varadhan, On the number of distinct sites visited by a random walk, Comm. Pure Appl. Math.32 (1979) 721-747. Zbl0418.60074MR539157
16. [16] N. Gantert, R. van der Hofstad, W. König, Deviations of a random walk in a random scenery with stretched exponential tails, Stochastic Process. Appl.116 (3) (2006) 480-492. Zbl1100.60056MR2199560
17. [17] J. Gärtner, On large deviations from the invariant measure, Theory Probab. Appl.22 (1) (1977) 24-39. Zbl0375.60033MR471040
18. [18] J.-P. Kahane, Some Random Series of Functions, second ed., Cambridge University Press, Cambridge, 1985. Zbl0571.60002MR833073
19. [19] H. Kesten, F. Spitzer, A limit theorem related to a new class of self-similar processes, Z. Wahrsch. Verw. Geb.50 (1979) 5-25. Zbl0396.60037MR550121
20. [20] W. König, P. Mörters, Brownian intersection local times: upper tail asymptotics and thick points, Ann. Probab.30 (2002) 1605-1656. Zbl1032.60073MR1944002
21. [21] E.H. Lieb, M. Loss, Analysis, Grad. Stud. Math., vol. 14, second ed., Amer. Math. Soc., Providence, RI, 2001. Zbl0966.26002MR1817225
22. [22] M. McLeod, J. Serrin, Uniqueness of solutions of semilinear Poisson equations, Proc. Natl. Acad. Sci. USA78 (11) (1981) 6592-6595. Zbl0474.35047MR634934
23. [23] V.V. Petrov, Sums of Independent Random Variables, Springer, Berlin, 1975. Zbl0322.60042MR388499
24. [24] F. Spitzer, Principles of Random Walk, second ed., Springer, Berlin, 1976. Zbl0359.60003MR388547
25. [25] K. Uchiyama, Green’s functions for random walks on $Z^N$, Proc. London Math. Soc.77 (3) (1998) 215-240. Zbl0893.60045MR1625467
26. [26] M.I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys.87 (1983) 567-576. Zbl0527.35023MR691044

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