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2006.51: On Levy Processes Conditioned to Stay Positive

2006.51: L. Chaumont and R.A. Doney (2006) On Levy Processes Conditioned to Stay Positive.

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Abstract

We construct the law of Levy processes conditioned to stay positive under general hypotheses. We obtain a Williams type path decomposition at the minimum of these processes. This result is then applied to prove the weak convergence of the law of Levy processes conditioned to stay positive as their initial state tends to 0. We describe an absolute continuity relationship between the limit law and the measure of the excursions away from 0 of the underlying Levy process reflected at its minimum. Then, when the Levy process creeps upwards, we study the lower tail at 0 of the law of the height this excursion.

Item Type:MIMS Preprint
Uncontrolled Keywords:Levy process conditioned to stay positive, path decomposition, weak convergence, excursion measure, creeping.
Subjects:MSC 2000 > 60 Probability theory and stochastic processes
MIMS number:2006.51
Deposited By:Dr Peter Neal
Deposited On:05 April 2006

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