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Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments. (English) Zbl 1292.60053

Summary: Let \(\{S_n:n\geq 0\}\) be a random walk with negative drift and \({\tau}(x)\) be the first time when the random walk crosses a given level \(x\geq 0\). This paper focuses on random walks with non-convolution equivalent increments. For this random walk, the uniform asymptotics of \(\operatorname{P}(S_{{\tau}(x)}-x>y, {\tau}(x)<\infty)\), as \(x\to \infty\), have been presented.

MSC:

60G50 Sums of independent random variables; random walks
60G51 Processes with independent increments; Lévy processes
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