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On the Mabinogion urn model

Part of: Stochastic processes Existence theories Markov processes

Published online by Cambridge University Press:  26 July 2018

David Stenlund
David Stenlund*
Affiliation:
Åbo Akademi University
*
* Postal address: Mathematics and Statistics, Faculty of Science and Engineering, Åbo Akademi University, Åbo, FIN-20500, Finland. Email address: david.stenlund@abo.fi
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Abstract

In this paper we discuss the Mabinogion urn model introduced by Williams (1991). Therein he describes an optimal control problem where the objective is to maximize the expected final number of objects of one kind in the Mabinogion urn model. Our main contribution is formulae for the expected time to absorption and its asymptotic behaviour in the optimally controlled process. We also present results for the noncontrolled Mabinogion urn process and briefly analyze other strategies that become superior if a certain discount factor is included.

Keywords

Mabinogion sheep problemMarkov chaindifference equationextinction timerandom walkhypergeometric functionbinomial identityDoob's h-transform

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 49J21: Optimal control problems involving relations other than differential equations 60G50: Sums of independent random variables; random walks
Type
Original Article
Information
Advances in Applied Probability , Volume 50 , Issue 2 , June 2018 , pp. 327 - 346
Copyright
Copyright © Applied Probability Trust 2018 

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