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Exceedance of power barriers for integrated continuous-time stationary ergodic stable processes

Part of: Stochastic processes Applications

Published online by Cambridge University Press:  01 July 2016

Uğur Tuncay Alparslan
Uğur Tuncay Alparslan*
Affiliation:
University of Nevada, Reno
*
∗ Current address: Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016, USA. Email address: tuncay.alparslan@american.edu
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Abstract

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We study the asymptotic behavior of the tail probability of integrated stable processes exceeding power barriers. In the first part of the paper the limiting behavior of the integrals of stable processes generated by ergodic dissipative flows is established. In the second part an example with the integral of a stable process generated by a conservative flow is analyzed. Finally, the difference in the order of magnitude of the exceedance probability in the two cases is related to the dependence structure of the underlying stable process.

Keywords

Continuous-time stationary stable processexceedance probabilitynonlinear barrierslong-range dependenceintegrated stable process

MSC classification

Primary: 60G52: Stable processes
Secondary: 62P05: Applications to actuarial sciences and financial mathematics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 3 , September 2009 , pp. 874 - 892
Copyright
Copyright © Applied Probability Trust 2009 

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