Hitting times of points for symmetric Levy processes

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 Levy processes are studied. The Levy measure is assumed to have completely monotone density function, and a scaling-type condition is imposed on the L´evy–Khintchine exponent Ψ. Proofs are based on generalised eigenfunction expansion for processes killed upon hitting the origin.

Electronic Journal of Probability