56 citations · 184 across the 23 of their papers we have counts for
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math.PR2005★ 11 cited
The principle of a single big jump: discrete and continuous time modulated random walks with heavy-tailed increments
Sergey Foss, Takis Konstantopoulos, Stan Zachary
We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to -infinity and that its increments (jumps) are…
math.PR2005★ 25 cited
The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk
Sergey Foss, Zbigniew Palmowski, Stan Zachary
We study the asymptotic probability that a random walk with heavy-tailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of As…