Limit theorem for random walk in weakly dependent random scenery

Details Limit theorem for random walk in weakly dependent random scenery Limit theorem for random walk in weakly dependent random scenery

2008-07-22

arxiv.org/abs/0807.3441v1

Mathematics

Probability

Scientific paper

Let $S=(S_k)_{k\geq 0}$ be a random walk on $\mathbb{Z}$ and $\xi=(\xi_{i})_{i\in\mathbb{Z}}$ a stationary random sequence of centered random variables, independent of $S$. We consider a random walk in random scenery that is the sequence of random variables $(\Sigma_n)_{n\geq 0}$ where $$\Sigma_n=\sum_{k=0}^n \xi_{S_k}, n\in\mathbb{N}.$$ Under a weak dependence assumption on the scenery $\xi$ we prove a functional limit theorem generalizing Kesten and Spitzer's theorem (1979).

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