Hitting times of points for symmetric Lévy processes with completely monotone jumps

Abstract

Small-space and large-time estimates and asymptotic expansion of the distribution function and (the derivatives of) the density function of hitting times of points for symmetric Lévy processes are studied. The Lévy measure is assumed to have completely monotone density function, and a scaling-type condition inf z Psi"(z) / Psi'(z) > 0 is imposed on the Lévy-Khintchine exponent Psi. Proofs are based on generalised eigenfunction expansion for processes killed upon hitting the origin.

24 pages

References in corpus (5)

• Barriers, exit time and survival probability for unimodal Lévy processes
• Hitting times of points and intervals for symmetric Lévy processes
• Penalising symmetric stable Lévy paths
• Rogers functions and fluctuation theory
• On harmonic function for the killed process upon hitting zero of asymmetric Lévy processes

Cited by in corpus (2)

• Asymptotic estimate of eigenvalues of pseudo-differential operators in an interval
• Boundary Harnack principle for the absolute value of a one-dimensional subordinate Brownian motion killed at $0$