Annealed deviations of random walk in random scenery

Gantert, Nina; König, Wolfgang; Shi, Zhan

doi:10.1016/j.anihpb.2005.12.002

Gantert, Nina ; König, Wolfgang ; Shi, Zhan

Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 1, pp. 47-76.

MR Zbl | 2 citations dans Numdam

DOI : 10.1016/j.anihpb.2005.12.002

@article{AIHPB_2007__43_1_47_0,
     author = {Gantert, Nina and K\"onig, Wolfgang and Shi, Zhan},
     title = {Annealed deviations of random walk in random scenery},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {47--76},
     publisher = {Elsevier},
     volume = {43},
     number = {1},
     year = {2007},
     doi = {10.1016/j.anihpb.2005.12.002},
     mrnumber = {2288269},
     zbl = {1119.60083},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2005.12.002/}
}

TY  - JOUR
AU  - Gantert, Nina
AU  - König, Wolfgang
AU  - Shi, Zhan
TI  - Annealed deviations of random walk in random scenery
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2007
SP  - 47
EP  - 76
VL  - 43
IS  - 1
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpb.2005.12.002/
DO  - 10.1016/j.anihpb.2005.12.002
LA  - en
ID  - AIHPB_2007__43_1_47_0
ER  -

%0 Journal Article
%A Gantert, Nina
%A König, Wolfgang
%A Shi, Zhan
%T Annealed deviations of random walk in random scenery
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2007
%P 47-76
%V 43
%N 1
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpb.2005.12.002/
%R 10.1016/j.anihpb.2005.12.002
%G en
%F AIHPB_2007__43_1_47_0

Gantert, Nina; König, Wolfgang; Shi, Zhan. Annealed deviations of random walk in random scenery. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 1, pp. 47-76. doi : 10.1016/j.anihpb.2005.12.002. http://archive.numdam.org/articles/10.1016/j.anihpb.2005.12.002/

Bibliographie
Cité par

[1] A. Asselah, F. Castell, Large deviations for Brownian motion in a random scenery, Probab. Theory Related Fields 126 (2003) 497-527. | MR | Zbl

[2] A. Asselah, F. Castell, A note on random walk in random scenery, preprint, 2005.

[3] A. Asselah, F. Castell, Self-intersection times for random walk, and random walk in random scenery in dimension $d \geq 5$ , preprint, 2005.

[4] G. Ben Arous, R. Léandre, Décroissance exponentielle du noyau de la chaleur sur la diagonale. II, Probab. Theory Related Fields 90 (3) (1991) 377-402. | MR | Zbl

[5] N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987. | MR | Zbl

[6] E. Bolthausen, A central limit theorem for two-dimensional random walks in random sceneries, Ann. Probab. 17 (1989) 108-115. | MR | Zbl

[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. | MR | Zbl

[8] A.N. Borodin, A limit theorem for sums of independent random variables defined on a recurrent random walk, Dokl. Akad. Nauk SSSR 246 (4) (1979) 786-787. | MR | Zbl

[9] D.C. Brydges, G. Slade, The diffusive phase of a model of self-interacting walks, Probab. Theory Related Fields 103 (1995) 285-315. | MR | Zbl

[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. | Numdam | MR | Zbl

[11] F. Castell, F. Pradeilles, Annealed large deviations for diffusions in a random shear flow drift, Stochastic Process Appl. 94 (2001) 171-197. | MR | Zbl

[12] X. Chen, Exponential asymptotics and law of the iterated logarithm for intersection local times of random walks, Ann. Probab. 32 (4) (2004). | MR | Zbl

[13] X. Chen, W. Li, Large and moderate deviations for intersection local times, Probab. Theory Related Fields 128 (2004) 213-254. | MR | Zbl

[14] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, second ed., Springer, Berlin, 1998. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[17] J. Gärtner, On large deviations from the invariant measure, Theory Probab. Appl. 22 (1) (1977) 24-39. | MR | Zbl

[18] J.-P. Kahane, Some Random Series of Functions, second ed., Cambridge University Press, Cambridge, 1985. | MR | Zbl

[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. | MR | Zbl

[20] W. König, P. Mörters, Brownian intersection local times: upper tail asymptotics and thick points, Ann. Probab. 30 (2002) 1605-1656. | MR | Zbl

[21] E.H. Lieb, M. Loss, Analysis, Grad. Stud. Math., vol. 14, second ed., Amer. Math. Soc., Providence, RI, 2001. | MR | Zbl

[22] M. Mcleod, J. Serrin, Uniqueness of solutions of semilinear Poisson equations, Proc. Natl. Acad. Sci. USA 78 (11) (1981) 6592-6595. | MR | Zbl

[23] V.V. Petrov, Sums of Independent Random Variables, Springer, Berlin, 1975. | MR | Zbl

[24] F. Spitzer, Principles of Random Walk, second ed., Springer, Berlin, 1976. | MR | Zbl

[25] K. Uchiyama, Green’s functions for random walks on $Z^{N}$ , Proc. London Math. Soc. 77 (3) (1998) 215-240. | MR | Zbl

[26] M.I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (1983) 567-576. | MR | Zbl

Cité par Sources :