In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5–25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561–575]. A random walk performs a motion in an i.i.d. environment and observes an i.i.d. scenery along its path. We assume that the scenery is in the domain of attraction of a stable distribution and prove that the resulting observations satisfy a limit theorem. The resulting limit process is a self-similar stochastic process with non-trivial dependencies.
Publié le : 2010-08-15
Classification:
birth–death process,
random environment,
random scenery,
random walk,
self-similar process
@article{1281099886,
author = {Franke, Brice and Saigo, Tatsuhiko},
title = {A self-similar process arising from a random walk with random environment in random scenery},
journal = {Bernoulli},
volume = {16},
number = {1},
year = {2010},
pages = { 825-857},
language = {en},
url = {http://dml.mathdoc.fr/item/1281099886}
}
Franke, Brice; Saigo, Tatsuhiko. A self-similar process arising from a random walk with random environment in random scenery. Bernoulli, Tome 16 (2010) no. 1, pp. 825-857. http://gdmltest.u-ga.fr/item/1281099886/