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Long range one-cookie random walk with positive speed

Author

Listed:
  • Collevecchio, Andrea
  • Hamza, Kais
  • Nguyen, Tuan-Minh

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.

Suggested Citation

  • Collevecchio, Andrea & Hamza, Kais & Nguyen, Tuan-Minh, 2021. "Long range one-cookie random walk with positive speed," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 462-478.
    • Handle: RePEc:eee:spapps:v:142:y:2021:i:c:p:462-478
    DOI: 10.1016/j.spa.2021.08.003
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