Long range one-cookie random walk with positive speed

Andrea Collevecchio, Kais Hamza and Tuan-Minh Nguyen

Stochastic Processes and their Applications, 2021, vol. 142, issue C, 462-478

Abstract: We study one-dimensional excited random walks with non-nearest neighbour jumps. When the process is at a vertex that has not been visited before, its next transition has a positive drift to the right, possibly with long jumps. Whenever the process visits a vertex that has already been visited in the past, its next transition is the one of a simple symmetric random walk. We give a sufficient condition for the process to have positive speed.

Keywords: Excited random walks; Self-interacting random walks (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.08.003

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