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On moments and tail behaviors of storage processes

Part of: Stochastic processes Stochastic analysis Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Arturo Kohatsu-Higa  and
Makoto Yamazato
Arturo Kohatsu-Higa*
Affiliation:
Universitat Pompeu Fabra
Makoto Yamazato*
Affiliation:
University of the Ryukyus
*
∗Postal address: Department of Economics, Universitat Pompeu Fabra, Ramón Trias Fargas, 25–27, 08005 Barcelona, Spain. Email address: kohatsu@upf.es
∗∗Postal address: Department of Mathematics, Faculty of Science, University of the Ryukyus, Senbaru1, Nishihara-cho, Okinawa, Japan 903-0213.
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Abstract

We study the existence of moments and the tail behavior of the densities of storage processes. We give sufficient conditions for existence and nonexistence of moments using the integrability conditions of submultiplicative functions with respect to Lévy measures. We then study the asymptotical behavior of the tails of these processes using the concave or convex envelope of the release rate function.

Keywords

Dam processstorage processsubordinatorsubmultiplicative functionsubexponentiality

MSC classification

Primary: 60G52: Stable processes 60H10: Stochastic ordinary differential equations 60J75: Jump processes 60K10: Applications (reliability, demand theory, etc.) 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003 , pp. 1069 - 1086
Copyright
Copyright © Applied Probability Trust 2003 

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