A self-similar process arising from a random walk with random environment in random scenery

Details A self-similar process arising from a random walk with random environment in random scenery A self-similar process arising from a random walk with random environment in random scenery

2011-02-25

arxiv.org/abs/1102.5241v1

Bernoulli 2010, Vol. 16, No. 3, 825-857

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ234 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ234

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.

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