Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T16:19:16.234Z Has data issue: false hasContentIssue false
  • English
  • Français

Explicit Gittins Indices for a Class of Superdiffusive Processes

Part of: Stochastic processes Operations research and management science 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: [email protected]
∗∗ Postal address: EPFL STI IPR LPM1, BM 3139 (Bâtiment BM), Station 17, CH-1015 Lausanne, Switzerland. Email address: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Bensoussan, A. and Lions, J. L. (1978). Applications des Inéquations Variationnelles en Contrôle Stochastique. Dunod, Paris.Google Scholar
Blanchard, Ph. and Hongler, M.-O. (2004). Quantum random walks and piecewise deterministic evolutions. Phys. Rev. Lett. 92, 120601, 4 pp.Google Scholar
Dusonchet, F. (2003). Dynamic scheduling for production systems operating in random environment. , EPFL.Google Scholar
Gittins, J. C. (1979). Bandit processes and dynamic allocation indices (with discussion). J. R. Statist. Soc. B 41, 148–177.Google Scholar
Gittins, J. C. and Jones, D. M. (1974). A dynamic allocation index for the sequential design of experiments. In Progress in Statistics, ed. Gani, J., North-Holland, Amsterdam, pp. 241–266.Google Scholar
Hongler, M.-O. (1979). Exact solutions of a class of nonlinear Fokker–Planck equations. Phys. Lett. A 75, 3–4.Google Scholar
Hongler, M.-O. (1979). Exact time dependent probability density for a nonlinear non-Markovian stochastic process. Helv. Phys. Acta 52, 280–287.Google Scholar
Hongler, M.-O. and Dusonchet, F. (2001). Optimal stopping and Gittins indices for piecewise deterministic evolution process. J. Discrete Events Systems 11, 235–248.Google Scholar
Hongler, M.-O., Filliger, R. and Blanchard, Ph. (2006). Soluble models for dynamics driven by a super-diffusive noise. Physica A 370, 301–315.Google Scholar
Itô, K. and McKean, H. P. Jr. (1974). Diffusion Processes and Their Sample Paths. Springer, Berlin.Google Scholar
Karatzas, I. (1984). Gittins indices in the dynamic allocation problem for diffusion processes. Ann. Prob. 12, 173–192.Google Scholar
Kaspi, H. and Mandelbaum, A. (1998). Multi armed bandits in discrete and continuous time. Ann. Appl. Prob. 8, 1270–1290.Google Scholar
Rogers, L. C. G. and Pitman, J. W. (1981). Markov Functions. Ann. Prob. 9, 573–582.Google Scholar
Whittle, P. (1980). Multi armed bandits and the Gittins index. J. R. Statist. Soc. B 42, 143–149.Google Scholar