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Distributional properties of solutions of dVt = Vt-dUt + dLt with Lévy noise

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Anita Diana Behme
Anita Diana Behme*
Affiliation:
Technische Universität Braunschweig
*
∗ Postal address: Institut für Mathematische Stochastik, Technische Universität Braunschweig, Pockelsstrasse 14, D-38106 Braunschweig, Germany. Email address: a.behme@tu-bs.de
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Abstract

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For a given bivariate Lévy process (Ut, Lt)t≥0, distributional properties of the stationary solutions of the stochastic differential equation dVt = Vt-dUt + dLt are analysed. In particular, the expectation and autocorrelation function are obtained in terms of the process (U, L) and in several cases of interest the tail behavior is described. In the case where U has jumps of size −1, necessary and sufficient conditions for the law of the solutions to be (absolutely) continuous are given.

Keywords

Stochastic differential equationgeneralized Ornstein-Uhlenbeck processstationaritymoment conditionstail behavior

MSC classification

Primary: 60G10: Stationary processes 60G51: Processes with independent increments; L'evy processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 3 , September 2011 , pp. 688 - 711
Copyright
Copyright © Applied Probability Trust 2011 

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