The sequential empirical process of a random walk in random scenery

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• 作者：Martin Wendler ^{martin.wendler@uni-greifswald.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60G50 ; 62G30 ; 60F17 ; 60G17
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：126
• 期：9
• 页码：2787-2799
• 全文大小：248 K

文摘

A random walk in random scenery (Y_n)_n∈N${\left(Y_n\right)}_{n\in \mathbb{N}}$ is given by Y_n=ξ_Sn$Y_n={\xi }_{S_n}$ for a random walk (S_n)_n∈N${\left(S_n\right)}_{n\in \mathbb{N}}$ and i.i.d. random variables (ξ_n)_n∈Z${\left({\xi }_n\right)}_{n\in \mathbb{Z}}$. In this paper, we will show the weak convergence of the sequential empirical process, i.e. the centered and rescaled empirical distribution function. The limit process shows a new type of behavior, combining properties of the limit in the independent case (roughness of the paths) and in the long range dependent case (self-similarity).