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

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

Alparslan UğuR Tuncay

Source: Adv. in Appl. Probab. Volume 41, Number 3 (2009), 874-892.

Abstract

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.

Primary Subjects: 60G52

Secondary Subjects: 62P05

Keywords: Continuous-time stationary stable process; exceedance probability; nonlinear barriers; long-range dependence; integrated stable process

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