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Stochastic Networks pp 197–214Cite as

Rare Events in the Presence of Heavy Tails

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Part of the book series: Lecture Notes in Statistics ((LNS,volume 117))

Abstract

We consider random walks and queues where one or more of the underlying distributions are heavy-tailed, more precisely subexponential (e.g., the tails are regularly varying, DFR Weibull type or lognormal type). This contrast the standard light-tailed assumptions (for example in large deviations theory) where exponential moments are required. The problem is to derive asymptotic expressions for rare events like large random walk maxima or large cycle maxima, large waiting times or large sojourn time in a network, or excursions above a large level, and also to study the behaviour of the process leading to the occurence of the rare event. The results support the folklore that in the heavy-tailed case, rare events occur as consequence of one big jump

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Authors
  1. Søren Asmussen
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Editors and Affiliations

  1. Department of Management Science and Operations Management, Columbia University, New York City, NY, 10027, USA

    Paul Glasserman

  2. Department of Operations Research and Industrial Engineering, Columbia University, New York City, NY, 10027, USA

    Karl Sigman  & David D. Yao  & 

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© 1996 Springer-Verlag New York, Inc.

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Asmussen, S. (1996). Rare Events in the Presence of Heavy Tails. In: Glasserman, P., Sigman, K., Yao, D.D. (eds) Stochastic Networks. Lecture Notes in Statistics, vol 117. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4062-4_10

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  • DOI: https://doi.org/10.1007/978-1-4612-4062-4_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94828-7

  • Online ISBN: 978-1-4612-4062-4

  • eBook Packages: Springer Book Archive

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