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

作者：Franke Brice^*; Saigo Tatsuhiko

来源：Bernoulli, 2010, 16(3): 825-857.

DOI：10.3150/09-BEJ234

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

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.

• 出版日期2010-8