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

Tomasz Juszczyszyn, Mateusz Kwaśnicki

Published 2014-03-14, updated 2015-04-17Version 2

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 L\'evy processes are studied. The L\'evy 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 L\'evy-Khintchine exponent Psi. Proofs are based on generalised eigenfunction expansion for processes killed upon hitting the origin.