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Invariance principle for biased bootstrap random walks

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  • Collevecchio, Andrea
  • Hamza, Kais
  • Liu, Yunxuan

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.

Suggested Citation

  • Collevecchio, Andrea & Hamza, Kais & Liu, Yunxuan, 2019. "Invariance principle for biased bootstrap random walks," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 860-877.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:3:p:860-877
    DOI: 10.1016/j.spa.2018.03.022
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    References listed on IDEAS

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    1. Collevecchio, Andrea & Hamza, Kais & Shi, Meng, 2016. "Bootstrap random walks," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1744-1760.
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