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A renewal-process-type expression for the moments of inverse subordinators

Part of: Distribution theory - Probability Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Andreas Nordvall Lagerås
Andreas Nordvall Lagerås*
Affiliation:
Stockholm University
*
∗Postal address: Department of Mathematics, Stockholm University, SE-10691 Stockholm, Sweden. Email address: andreas@math.su.se
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Abstract

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We define an inverse subordinator as the passage times of a subordinator to increasing levels. It has previously been noted that such processes have many similarities to renewal processes. Here we present an expression for the joint moments of the increments of an inverse subordinator. This is an analogue of a result for renewal processes. The main tool is a theorem on processes which are both renewal processes and Cox processes.

Keywords

Subordinatorpassage timerenewal theoryCox processlocal time

MSC classification

Primary: 60K05: Renewal theory
Secondary: 60G51: Processes with independent increments; L'evy processes 60G55: Point processes 60E07: Infinitely divisible distributions; stable distributions
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 1134 - 1144
Copyright
© Applied Probability Trust 2005 

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