Abstract
We consider a random walk {S n} 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 {S n} 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.
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Korshunov, D.A., Schlegel, S. & Schmidt, V. Asymptotics for Random Walks with Dependent Heavy-Tailed Increments. Siberian Mathematical Journal 44, 833–844 (2003). https://doi.org/10.1023/A:1025940920770
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DOI: https://doi.org/10.1023/A:1025940920770