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Explicit Gittins Indices for a Class of Superdiffusive Processes

Part of: Operations research and management science Stochastic processes Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Roger Filliger  and
Max-Olivier Hongler
Roger Filliger*
Affiliation:
Universität Bielefeld
Max-Olivier Hongler*
Affiliation:
Ecole Polytechnique Fédérale de Lausanne
*
∗ Postal address: Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany. Email address: filliger@physik.uni-bielefeld.de
∗∗ Postal address: EPFL STI IPR LPM1, BM 3139 (Bâtiment BM), Station 17, CH-1015 Lausanne, Switzerland. Email address: max.hongler@epfl.ch
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Abstract

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We explicitly calculate the dynamic allocation indices (i.e. the Gittins indices) for multi-armed Bandit processes driven by superdiffusive noise sources. This class of model generalizes former results derived by Karatzas for diffusive processes. In particular, the Gittins indices do, in this soluble class of superdiffusive models, explicitly depend on the noise state.

Keywords

Gittins indexoptimal stoppingsuperdiffusion

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 90B36: Scheduling theory, stochastic 93E20: Optimal stochastic control
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 2 , June 2007 , pp. 554 - 559
Copyright
Copyright © Applied Probability Trust 2007 

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