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

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...

Full description

Saved in:
Bibliographic Details
Published inStochastic processes and their applications Vol. 129; no. 10; pp. 3748 - 3773
Main Author Forien, Raphaël
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2019
Elsevier
Subjects
Barriers to gene flow
Generalised Brownian motions
Life Sciences
Partial reflection
Random walks with obstacles
Vegetal Biology
60J65
60G99
60F99
Partial reflection
Generalised Brownian motions
60J70
Random walks with obstacles
Barriers to gene flow
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2018.10.006