Electronic Journal of Probability

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

Tomasz Juszczyszyn and Mateusz Kwaśnicki

Full-text: Open access

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

Permanent link to this document
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

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes
Secondary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
Lévy process hitting time of points completely monotone jumps complete Bernstein function subordinate Brownian motion

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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