most citedAsymptotics for first-passage times of Lévy processes and random walks

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math.PR2007★ 3 cited

Asymptotics for first-passage times of Lévy processes and random walks

Denis Denisov, Vsevolod Shneer

We study the exact asymptotics for the distribution of the first time a Lévy process crosses a negative level . We prove that $\mathbf P(τ_x>t)\sim V(x)\mathbf P(X_…

math.PR2007★ 124 cited

Large deviations for random walks under subexponentiality: the big-jump domain

D. Denisov, A. B. Dieker, V. Shneer

For a given one-dimensional random walk with a subexponential step-size distribution, we present a unifying theory to study the sequences for which $\mathsf{P}\…