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 ${\tau }_x$ a Lévy process $X_t$ crosses a negative level $-x$. We prove that $\mathbf P(τ_x>t)\sim V(x)\mathbf P(X_…