• Bernoulli
  • Volume 16, Number 3 (2010), 825-857.

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

Brice Franke and Tatsuhiko Saigo

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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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Bernoulli, Volume 16, Number 3 (2010), 825-857.

First available in Project Euclid: 6 August 2010

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birth–death process random environment random scenery random walk self-similar process


Franke, Brice; Saigo, Tatsuhiko. A self-similar process arising from a random walk with random environment in random scenery. Bernoulli 16 (2010), no. 3, 825--857. doi:10.3150/09-BEJ234.

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