The distribution of the supremum for spectrally asymmetric Lévy processes

Zbigniew Michna , Zbigniew Palmowski , Martijn Pistorius

Abstract

In this article we derive formulas for the probability P(supt u), T > 0 and P(supt<1 X(t) > u) where X is a spectrally positive Lévy process with infinite variation. The formulas are generalizations of the well-known Takács formulas for stochastic processes with non-negative and interchangeable increments. Moreover, we find the joint distribution of inft
Author Zbigniew Michna (MISaF / IZM / KMiC)
Zbigniew Michna,,
- Katedra Matematyki i Cybernetyki
, Zbigniew Palmowski - [University of Wroclaw]
Zbigniew Palmowski,,
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, Martijn Pistorius - [Imperial College London]
Martijn Pistorius,,
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Journal seriesElectronic Communications in Probability, ISSN 1083-589X, (A 20 pkt)
Issue year2015
Vol20
No24
Pages1-10
Publication size in sheets0.5
Keywords in EnglishLévy process; distribution of the supremum of a stochastic process; spectrally asymmetric Lévy process
ASJC Classification1804 Statistics, Probability and Uncertainty; 2613 Statistics and Probability
DOIDOI:10.1214/ECP.v20-2999
Languageen angielski
File
Michna.Palmowski.Pistorius_The distribution.pdf 215,11 KB
Score (nominal)20
Score sourcejournalList
Publication indicators Scopus Citations = 3; Scopus SNIP (Source Normalised Impact per Paper): 2015 = 0.859; WoS Impact Factor: 2015 = 0.467 (2) - 2015=0.669 (5)
Citation count*7 (2019-12-08)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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