We describe a new class of self-similar symmetric α-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting models are different from the ones studied earlier both in their memory properties and smoothness of the sample paths.
Publié le : 2006-08-14
Classification:
Stable process,
self-similar process,
stationary process,
integral representation,
conservative flow,
null flow,
fractional Brownian motion,
local time,
random reward,
chaos expansion,
superposition of scaled inputs,
long memory,
60G18,
60G52,
60G17
@article{1159804987,
author = {Cohen, Serge and Samorodnitsky, Gennady},
title = {Random rewards, fractional Brownian local times and stable self-similar processes},
journal = {Ann. Appl. Probab.},
volume = {16},
number = {1},
year = {2006},
pages = { 1432-1461},
language = {en},
url = {http://dml.mathdoc.fr/item/1159804987}
}
Cohen, Serge; Samorodnitsky, Gennady. Random rewards, fractional Brownian local times and stable self-similar processes. Ann. Appl. Probab., Tome 16 (2006) no. 1, pp. 1432-1461. http://gdmltest.u-ga.fr/item/1159804987/