We define the reflection of a random walk at a general barrier and derive, in case the increments are light tailed and have negative mean, a necessary and sufficient criterion for the global maximum of the reflected process to be finite a.s. If it is finite a.s., we show that the tail of the distribution of the global maximum decays exponentially fast and derive the precise rate of decay. Finally, we discuss an example from structural biology that motivated the interest in the reflection at a general barrier.
Publié le : 2006-02-14
Classification:
Exponential change of measure,
global maximum,
nonlinear renewal theory,
random walk,
reflection,
structural biology,
60G70,
60F10
@article{1141654279,
author = {Hansen, Niels Richard},
title = {The maximum of a random walk reflected at a general barrier},
journal = {Ann. Appl. Probab.},
volume = {16},
number = {1},
year = {2006},
pages = { 15-29},
language = {en},
url = {http://dml.mathdoc.fr/item/1141654279}
}
Hansen, Niels Richard. The maximum of a random walk reflected at a general barrier. Ann. Appl. Probab., Tome 16 (2006) no. 1, pp. 15-29. http://gdmltest.u-ga.fr/item/1141654279/