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A piecewise linear stochastic differential equation driven by a Lévy process

Part of: Stochastic analysis Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Josh Reed  and
Bert Zwart
Josh Reed
Affiliation:
New York University, Leonard N. Stern School of Business, New York University, Kaufman Management Center, 44 West 4th Street, Suite 8–79, New York, NY 10012, USA. Email address: jreed@stern.nyu.edu
Bert Zwart
Affiliation:
CWI, VU University, EURANDOM and Georgia Institute of Technology, CWI, Science Park 123, 1098 XG, Amsterdam, The Netherlands. Email address: bertz@cwi.nl
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Abstract

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We consider a stochastic differential equation (SDE) with piecewise linear drift driven by a spectrally one-sided Lévy process. We show that this SDE has some connections with queueing and storage models, and we use this observation to obtain the invariant distribution.

Keywords

Lévy processqueues with many serversstorage modelstochastic differential equationmartingaletime change

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 60G51: Processes with independent increments; L'evy processes 60H35: Computational methods for stochastic equations 60K25: Queueing theory
Type
Part 2. Lévy Processes
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 109 - 119
Copyright
Copyright © Applied Probability Trust 2011 

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