Electronic Communications in Probability

Short proofs in extrema of spectrally one sided Lévy processes

Loïc Chaumont and Jacek Małecki

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We provide short and simple proofs of the continuous time ballot theorem for processes with cyclically interchangeable increments and Kendall’s identity for spectrally positive Lévy processes. We obtain the later result as a direct consequence of the former. The ballot theorem is extended to processes having possible negative jumps. Then we prove through straightforward arguments based on the law of bridges and Kendall’s identity, Theorem 2.4 in [20] which gives an expression for the law of the supremum of spectrally positive Lévy processes. An analogous formula is obtained for the supremum of spectrally negative Lévy processes.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 55, 12 pp.

Received: 17 April 2018
Accepted: 10 August 2018
First available in Project Euclid: 1 September 2018

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Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes 60G09: Exchangeability

cyclically interchangeable process spectrally one sided Lévy process Ballot theorem Kendall’s identity past supremum bridge

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Chaumont, Loïc; Małecki, Jacek. Short proofs in extrema of spectrally one sided Lévy processes. Electron. Commun. Probab. 23 (2018), paper no. 55, 12 pp. doi:10.1214/18-ECP163. https://projecteuclid.org/euclid.ecp/1535767266

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