Electronic Journal of Probability

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

Tomasz Juszczyszyn and Mateusz Kwaśnicki

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

This work is licensed under aCreative Commons Attribution 3.0 License.


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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