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arXiv 2014-03-14 DOI 10.1214/EJP.v20-3440 0 views

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

Juszczyszyn, Tomasz · Kwaśnicki, Mateusz

Original · EN

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.

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