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Siberian Mathematical Journal

, Volume 44, Issue 5, pp 833–844 | Cite as

Asymptotics for Random Walks with Dependent Heavy-Tailed Increments

  • D. A. Korshunov
  • S. Schlegel
  • V. Schmidt
Article

Abstract

We consider a random walk {Sn} with dependent heavy-tailed increments and negative drift. We study the asymptotics for the tail probability P{sup n S n >x} as x→∞. If the increments of {Sn} are independent then the exact asymptotic behavior of P{sup n S n >x} is well known. We investigate the case in which the increments are given as a one-sided asymptotically stationary linear process. The tail behavior of sup n S n turns out to depend heavily on the coefficients of this linear process.

random walk dependent increment heavy tails subexponential distribution tail asymptotics 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • D. A. Korshunov
    • 1
  • S. Schlegel
    • 2
  • V. Schmidt
    • 3
  1. 1.Sobolev Institute of MathematicsNovosibirsk
  2. 2.EindhovenThe Netherlands
  3. 3.University of UlmGermany

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