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PROGRESS AND PROBLEMS IN THE THEORY OF REGENERATIVE PHENOMENA

Published online by Cambridge University Press:  19 December 2006

J. F. C. KINGMAN
J. F. C. KINGMAN
Affiliation:
Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, United [email protected]
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Abstract

Regenerative phenomena were introduced some forty years ago to address problems in the theory of continuous-time Markov processes. The early work in the theory left a number of difficult unsolved problems, in the classification of $p$-functions, oscillation and inequalities, the multiplicative theory, and the theory of unbounded semi-$p$-functions. Recent years have shown progress on all of these fronts, and this paper surveys these results, while drawing attention to significant problems that remain open.

Keywords

60J25 (primary)26A51 (secondary)
Type
Survey
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 6 , December 2006 , pp. 881 - 896
Copyright
The London Mathematical Society 2006

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