Gene flow across geographical barriers — scaling limits of random walks with obstacles

Raphaël Forien

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 3748-3773

Abstract: We study a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. We obtain a non trivial scaling limit which behaves like reflected Brownian motion until its local time at zero reaches an exponential variable. It then follows reflected Brownian motion on the other side of the origin until its local time at zero reaches another exponential level, etc. These random walks are used in population genetics to trace the position of ancestors in the past near geographical barriers.

Keywords: Generalised Brownian motions; Random walks with obstacles; Partial reflection; Barriers to gene flow (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.10.006

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