Electronic Communications in Probability

On the result of Doney

Tibor Pogany and Saralees Nadarajah

Full-text: Open access

Abstract

Let $X$ denote a spectrally positive stable process of index $\alpha \in $.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 58, 4 pp.

Dates
Accepted: 14 August 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320985

Digital Object Identifier
doi:10.1214/ECP.v20-4081

Mathematical Reviews number (MathSciNet)
MR3384116

Zentralblatt MATH identifier
1327.60104

Keywords
Asymptotic behavior Stable process Wright generalized hypergeometric $\Psi$ function

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Pogany, Tibor; Nadarajah, Saralees. On the result of Doney. Electron. Commun. Probab. 20 (2015), paper no. 58, 4 pp. doi:10.1214/ECP.v20-4081. https://projecteuclid.org/euclid.ecp/1465320985


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References

  • Bernyk, Violetta; Dalang, Robert C.; Peskir, Goran. The law of the supremum of a stable Lévy process with no negative jumps. Ann. Probab. 36 (2008), no. 5, 1777–1789.
  • Bertoin, Jean. Lévy processes. Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0
  • Braaksma, B. L. J. Asymptotic expansions and analytic continuations for a class of Barnes-integrals. Compositio Math. 15 1964 239–341 (1964).
  • Doney, R. A. A note on the supremum of a stable process. Stochastics 80 (2008), no. 2-3, IMS Lecture Notes—Monograph Series, 151–155.
  • Kilbas, Anatoly A.; Srivastava, Hari M.; Trujillo, Juan J. Theory and applications of fractional differential equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006. xvi+523 pp. ISBN: 978-0-444-51832-3; 0-444-51832-0
  • Sato, Ken-iti. Lévy processes and infinitely divisible distributions. Translated from the 1990 Japanese original. Revised by the author. Cambridge Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999. xii+486 pp. ISBN: 0-521-55302-4
  • E. M. Wright, The asymptotic expansion of the generalized hypergeometric function, Journal of the London Mathematical Society, (1935), 10, 286-293.