Electronic Communications in Probability

Generalized scale functions of standard processes with no positive jumps

Kei Noba

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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

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

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

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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

standard process scale function excursion theory spectrally negative Lévy process

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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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