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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 80, 2008 - Issue 2-3: A Festschrift for Priscilla Greenwood
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Original Articles

A note on the supremum of a stable process

R.A. Doney The University of Manchester, Manchester, UKCorrespondence[email protected]
Pages 151-155 | Received 01 Oct 2007, Accepted 27 Nov 2007, Published online: 09 Oct 2008

Citations (17)

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Thomas Simon. (2011) Hitting densities for spectrally positive stable processes. Stochastics 83:2, pages 203-214.
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Articles from other publishers (16)

Jorge Ignacio González Cázares, Arturo Kohatsu-Higa & Aleksandar Mijatović. (2023) Joint density of the stable process and its supremum: Regularity and upper bounds. Bernoulli 29:4.
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Benjamin De Bruyne, Satya N Majumdar & Grégory Schehr. (2021) Expected maximum of bridge random walks & Lévy flights. Journal of Statistical Mechanics: Theory and Experiment 2021:8, pages 083215.
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Loïc Chaumont & Andreas E. Kyprianou. 2021. A Lifetime of Excursions Through Random Walks and Lévy Processes. A Lifetime of Excursions Through Random Walks and Lévy Processes 1 11 .
Jorge I. González Cázares, Aleksandar Mijatović & Gerónimo Uribe Bravo. (2019) Exact simulation of the extrema of stable processes. Advances in Applied Probability 51:4, pages 967-993.
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Yulin Song & Yingchao Xie. (2017) Existence of Density Functions for the Running Maximum of a Lévy-Itô Diffusion. Potential Analysis 48:1, pages 35-48.
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Tibor Pogany & Saralees Nadarajah. (2015) On the result of Doney. Electronic Communications in Probability 20:none.
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A. Kuznetsov. (2013) On the density of the supremum of a stable process. Stochastic Processes and their Applications 123:3, pages 986-1003.
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Violetta Bernyk, Robert C. Dalang & Goran Peskir. (2011) Predicting the ultimate supremum of a stable Lévy process with no negative jumps. The Annals of Probability 39:6.
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Alexey Kuznetsov. (2011) On extrema of stable processes. The Annals of Probability 39:3.
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Zbigniew Michna. (2011) Formula for the supremum distribution of a spectrally positive -stable Lévy process. Statistics & Probability Letters 81:2, pages 231-235.
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Friedrich Hubalek & Alexey Kuznetsov. (2011) A convergent series representation for the density of the supremum of a stable process. Electronic Communications in Probability 16:none.
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Kouji Yano, Yuko Yano & Marc Yor. (2010) Penalisation of a stable Lévy process involving its one-sided supremum. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 46:4.
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R. A. Doney & M. S. Savov. (2010) The asymptotic behavior of densities related to the supremum of a stable process. The Annals of Probability 38:1.
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P. Patie. (2009) A few remarks on the supremum of stable processes. Statistics & Probability Letters 79:8, pages 1125-1128.
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Violetta Bernyk, Robert C. Dalang & Goran Peskir. (2008) The law of the supremum of a stable Lévy process with no negative jumps. The Annals of Probability 36:5.
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Goran Peskir. (2008) The Law of the Hitting Times to Points by a Stable Lévy Process with No Negative Jumps. Electronic Communications in Probability 13:none.
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