Invariance principle for biased bootstrap random walks

Andrea Collevecchio, Kais Hamza and Yunxuan Liu

Stochastic Processes and their Applications, 2019, vol. 129, issue 3, 860-877

Abstract: Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (dependent) Bernoulli random variables is produced. It is built, from the original sequence, according to a cellular automata rule. Equipped with these two sequences, we construct two more according to the same cellular automata rule. The construction is repeated a fixed number of times yielding an infinite array ({−K,…,K}×N) of (dependent) Bernoulli random variables. Taking partial sums of these sequences, we obtain a (2K+1)-dimensional process whose increments belong to the state space {−1,1}2K+1.

Keywords: Random walks; Bootstrap random walks; Functional limit theorem (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.03.022

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