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Extremal problems for regenerative phenomena

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

J. F. C. Kingman
J. F. C. Kingman*
Affiliation:
Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, UK. Email address: director@newton.cam.ac.uk
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Abstract

This paper explores the possibility of a calculus of variations powerful enough to prove inequalities for the p-functions of regenerative phenomena such as that conjectured by Davidson and proved by Dai. It is shown that this is unlikely to be achieved by compactifying the space of standard p-functions, and a more promising approach is that of working in a compact subspace. The analysis leads to a class of candidate p-functions which contains all the maxima of general functionals.

Keywords

Inequalities for p-functionscalculus of variationscompact function spaces

MSC classification

Primary: 60J99: None of the above, but in this section
Type
Part 6. Stochastic processes
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 333 - 346
Copyright
Copyright © Applied Probability Trust 2004 

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