Passage of Lévy Processes across Power Law Boundaries at Small Times

Jean Bertoin, Ronald A. Doney, Ross A. Maller

We wish to characterise when a Lévy process $X_t$ crosses boundaries like $t^{\kappa }$, $\kappa >0$, in a one or two-sided sense, for small times $t$; thus, we enquire when $\limsup_{t\downarro…