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First passage properties of a generalized Pólya urn

Kearney, Michael and Martin, RJ (2016) First passage properties of a generalized Pólya urn Journal of Statistical Mechanics: Theory and Experiment, 2016, 123407.

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Abstract

A generalized two-component Pólya urn process, parameterized by a variable a , is studied in terms of the likelihood that due to fluctuations the initially smaller population in a scenario of competing population growth eventually becomes the larger, or is the larger after a certain passage of time. By casting the problem as an inhomogeneous directed random walk we quantify this role-reversal phenomenon through the first passage probability that equality in size is first reached at a given time, and the related exit probability that equality in size is reached no later than a given time. Using an embedding technique, exact results are obtained which complement existing results and provide new insights into behavioural changes (akin to phase transitions) which occur at defined values of a .

Item Type: Article
Subjects : Physics
Divisions : Faculty of Engineering and Physical Sciences > Physics
Authors :
NameEmailORCID
Kearney, MichaelM.J.Kearney@surrey.ac.ukUNSPECIFIED
Martin, RJUNSPECIFIEDUNSPECIFIED
Date : 22 December 2016
Identification Number : 10.1088/1742-5468/2016/12/123407
Copyright Disclaimer : © 2016 IOP Publishing Ltd and SISSA Medialab sr. This is an author-created, un-copyedited version of an article accepted for publication in Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at [insert DOI]
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 18 Nov 2016 12:09
Last Modified : 18 Jul 2017 14:51
URI: http://epubs.surrey.ac.uk/id/eprint/812896

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