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First exit time of a Lévy flight from a bounded region in ℝN

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  30 March 2016

Yoora Kim ,
Irem Koprulu  and
Ness B. Shroff
Yoora Kim*
Affiliation:
University of Ulsan
Irem Koprulu*
Affiliation:
The Ohio State University
Ness B. Shroff*
Affiliation:
The Ohio State University
*
∗ Postal address: Department of Mathematics, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, South Korea. Email address: [email protected]
∗∗ Postal address: Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA. Email address: [email protected]
∗∗∗ Postal address: Departments of Electrical and Computer Engineering and Computer Science and Engineering, The Ohio State University, Columbus, OH 43210, USA. Email address: [email protected]
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Abstract

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In this paper we characterize the mean and the distribution of the first exit time of a Lévy flight from a bounded region in N-dimensional spaces. We characterize tight upper and lower bounds on the tail distribution of the first exit time, and provide the exact asymptotics of the mean first exit time for a given range of step-length distribution parameters.

Keywords

Lévy flightfirst exit timefirst passage timebounded region

MSC classification

Primary: 60J75: Jump processes
Secondary: 60G50: Sums of independent random variables; random walks
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 649 - 664
Copyright
Copyright © 2015 by the Applied Probability Trust 

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