## Electronic Journal of Probability

### 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 $\mathrm{inf} \xi \Psi"(\xi) / \Psi'(\xi) > 0$ is imposed on the Lévy-Khintchine exponent $\Psi$. Proofs are based on generalised eigenfunction expansion for processes killed upon hitting the origin.

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 48, 24 pp.

Dates
Accepted: 25 April 2015
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465067154

Digital Object Identifier
doi:10.1214/EJP.v20-3440

Mathematical Reviews number (MathSciNet)
MR3339868

Zentralblatt MATH identifier
1321.60094

Rights

#### Citation

Juszczyszyn, Tomasz; Kwaśnicki, Mateusz. Hitting times of points for symmetric Lévy processes with completely monotone jumps. Electron. J. Probab. 20 (2015), paper no. 48, 24 pp. doi:10.1214/EJP.v20-3440. https://projecteuclid.org/euclid.ejp/1465067154

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