On Wiener–Hopf factors for stable processes

Piotr Graczyk; Tomasz Jakubowski

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 1, page 9-19
  • ISSN: 0246-0203

Abstract

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We give a series representation of the logarithm of the bivariate Laplace exponent κ of α-stable processes for almost all α ∈ (0, 2].

How to cite

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Graczyk, Piotr, and Jakubowski, Tomasz. "On Wiener–Hopf factors for stable processes." Annales de l'I.H.P. Probabilités et statistiques 47.1 (2011): 9-19. <http://eudml.org/doc/241592>.

@article{Graczyk2011,
abstract = {We give a series representation of the logarithm of the bivariate Laplace exponent κ of α-stable processes for almost all α ∈ (0, 2].},
author = {Graczyk, Piotr, Jakubowski, Tomasz},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stable process; Wiener–Hopf factorization; Wiener-Hopf factorization},
language = {eng},
number = {1},
pages = {9-19},
publisher = {Gauthier-Villars},
title = {On Wiener–Hopf factors for stable processes},
url = {http://eudml.org/doc/241592},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Graczyk, Piotr
AU - Jakubowski, Tomasz
TI - On Wiener–Hopf factors for stable processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 1
SP - 9
EP - 19
AB - We give a series representation of the logarithm of the bivariate Laplace exponent κ of α-stable processes for almost all α ∈ (0, 2].
LA - eng
KW - stable process; Wiener–Hopf factorization; Wiener-Hopf factorization
UR - http://eudml.org/doc/241592
ER -

References

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  9. [9] P. Graczyk and T. Jakubowski. On exit time of symmetric α-stable processes. Preprint, 2009. MR2779394
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  11. [11] A. Kuznetsov. Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes. J. Appl. Probab. (2009). To appear. Zbl1222.60038MR2752893
  12. [12] A. E. Kyprianou. Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer, Berlin, 2006. Zbl1104.60001MR2250061
  13. [13] A. E. Kyprianou and Z. Palmowski. Fluctuations of spectrally negative Markov additive processes. In Séminaire de probabilités XLI. Lecture Notes in Math. 1934121–135. Springer, Berlin, 2008. Zbl1156.60060MR2483728
  14. [14] M. Waldschmidt. Private communication, 2009. 

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