Electronic Communications in Probability

Generalized scale functions of standard processes with no positive jumps

Kei Noba

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Abstract

As a generalization of scale functions of spectrally negative Lévy processes, we define generalized scale functions of general standard processes with no positive jumps. For this purpose, we utilize the excursion theory. Using the generalized scale functions, we study Laplace transforms of hitting times, potential measures and duality.

Article information

Source
Electron. Commun. Probab., Volume 25 (2020), paper no. 8, 12 pp.

Dates
Received: 1 June 2018
Accepted: 17 January 2020
First available in Project Euclid: 29 January 2020

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1580266866

Digital Object Identifier
doi:10.1214/20-ECP289

Subjects
Primary: 60J99: None of the above, but in this section 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60G51: Processes with independent increments; Lévy processes

Keywords
standard process scale function excursion theory spectrally negative Lévy process

Rights
Creative Commons Attribution 4.0 International License.

Citation

Noba, Kei. Generalized scale functions of standard processes with no positive jumps. Electron. Commun. Probab. 25 (2020), paper no. 8, 12 pp. doi:10.1214/20-ECP289. https://projecteuclid.org/euclid.ecp/1580266866


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