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Asymptotics for random walks with dependent heavy-tailed increments

机译:具有依赖的重尾增量的随机行走的渐近性

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摘要

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_nS_n > x} as x → ∞. If the increments of {S_n} are independent then the exact asymptotic behavior of P{sup_nS_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_nS_n turns out to depend heavily on the coefficients of this linear process.
机译:我们考虑具有相关的重尾增量和负漂移的随机游走{S_n}。我们研究了当x→∞时,尾部概率P {sup_nS_n> x}的渐近性。如果{S_n}的增量是独立的,则众所周知P {sup_nS_n> x}的精确渐近行为。我们调查的情况下,增量为单边渐近平稳线性过程。 sup_nS_n的尾部行为在很大程度上取决于此线性过程的系数。

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