Journal
STATISTICS & PROBABILITY LETTERS
Volume 80, Issue 7-8, Pages 697-705Publisher
ELSEVIER
DOI: 10.1016/j.spl.2010.01.002
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Funding
- NSF [DMS-0505747, DMS-0706786, DGE-0221680]
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Let {D(s), s >= 0} be a Levy subordinator, that is, a non-decreasing process with stationary and independent increments and suppose that D(0) = 0. We study the first-hitting time of the process D, namely, the process E(t) = inf{s : D(s) > t}, t >= 0. The process E is, in general, non-Markovian with non-stationary and non-independent increments. We derive a partial differential equation for the Laplace transform of the n-time tail distribution function P[E(t(1)) > s(1), ... , E(t(n)) > s(n)]. This PDE can be used to derive all n-time moments of the process E. As an application, we give a recursive formula for multiple-time moments of the local time of a Markov process in terms of its transition density. (C) 2010 Elsevier B.V. All rights reserved.
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