Abstract
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.
Citation
Brice Franke. Tatsuhiko Saigo. "A self-similar process arising from a random walk with random environment in random scenery." Bernoulli 16 (3) 825 - 857, August 2010. https://doi.org/10.3150/09-BEJ234
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