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Deviations of a random walk in a random scenery with stretched exponential tails
- Source :
-
Stochastic Processes & Their Applications . Mar2006, Vol. 116 Issue 3, p480-492. 13p. - Publication Year :
- 2006
-
Abstract
- Abstract: Let be a d-dimensional random walk in random scenery, i.e., with a random walk in and an i.i.d. scenery, independent of the walk. We assume that the random variables have a stretched exponential tail. In particular, they do not possess exponential moments. We identify the speed and the rate of the logarithmic decay of for all sequences satisfying a certain lower bound. This complements results of Gantert et al. [Annealed deviations of random walk in random scenery, preprint, 2005], where it was assumed that has exponential moments of all orders. In contrast to the situation (Gantert et al., 2005), the event is not realized by a homogeneous behavior of the walk''s local times and the scenery, but by many visits of the walker to a particular site and a large value of the scenery at that site. This reflects a well-known extreme behavior typical for random variables having no exponential moments. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 03044149
- Volume :
- 116
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Stochastic Processes & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 19598567
- Full Text :
- https://doi.org/10.1016/j.spa.2005.10.006