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Discrete Random Walks

In: Random Walk and Diffusion Models

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  • Wolf Schwarz

    (University of Potsdam, Research Methods in Human Sciences)

Abstract

We consider and analyze processes moving in discrete time steps through a discrete state space. For simple random walks with and without a drift component, we show how to derive in an elementary manner basic quantities such as absorption probabilities and (conditional) mean first-passage times, and we explain the role of generating functions in that context. We then show how these analyses generalize to more complex processes such as correlated random walks, the Ehrenfest model, or the Fisher–Wright model of random genetic drift.

Suggested Citation

  • Wolf Schwarz, 2022. "Discrete Random Walks," Springer Books, in: Random Walk and Diffusion Models, chapter 0, pages 13-54, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-12100-5_2
    DOI: 10.1007/978-3-031-12100-5_2
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