Asymptotics of a Dynamic Random Walk in a Random Scenery: II. A Functional Limit Theorem

#### N. Guillotin-Plantard

1999, v.5, №2, 201-218

ABSTRACT

Let $(S_{n})_{n\in{ N}}$ be a $Z$-random walk on nearest neighbours with dynamical quasiperiodic transition probabilities in a random scenery $\xi(\alpha),\alpha\in Z$, that is a family of i.i.d. random variables, independent of the random walk. It is shown that $\displaystyle n^{-\frac{3}{4}}\sum_{i=0}^{[nt]} \xi(S_{i})$ converges weakly as $n\rightarrow \infty$ to a self-similar process with stationary increments.

Keywords: random walk,random scenery,local time,Brownian motion,functional limittheorem