Nous donnons un développement en série du logarithme de l'exposant de Laplace bivarié κ des processus α-stables pour presque tous α ∈ (0, 2].
We give a series representation of the logarithm of the bivariate Laplace exponent κ of α-stable processes for almost all α ∈ (0, 2].
Mots-clés : stable process, Wiener-Hopf factorization
@article{AIHPB_2011__47_1_9_0, author = {Graczyk, Piotr and Jakubowski, Tomasz}, title = {On {Wiener-Hopf} factors for stable processes}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {9--19}, publisher = {Gauthier-Villars}, volume = {47}, number = {1}, year = {2011}, doi = {10.1214/09-AIHP348}, mrnumber = {2779394}, zbl = {1208.60044}, language = {en}, url = {http://archive.numdam.org/articles/10.1214/09-AIHP348/} }
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 SP - 9 EP - 19 VL - 47 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/articles/10.1214/09-AIHP348/ DO - 10.1214/09-AIHP348 LA - en ID - AIHPB_2011__47_1_9_0 ER -
%0 Journal Article %A Graczyk, Piotr %A Jakubowski, Tomasz %T On Wiener-Hopf factors for stable processes %J Annales de l'I.H.P. Probabilités et statistiques %D 2011 %P 9-19 %V 47 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/articles/10.1214/09-AIHP348/ %R 10.1214/09-AIHP348 %G en %F AIHPB_2011__47_1_9_0
Graczyk, Piotr; Jakubowski, Tomasz. On Wiener-Hopf factors for stable processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 1, pp. 9-19. doi : 10.1214/09-AIHP348. http://archive.numdam.org/articles/10.1214/09-AIHP348/
[1] A Concise Introduction to the Theory of Numbers. Cambridge Univ. Press, Cambridge, 1984. | MR | Zbl
.[2] The law of the supremum of a stable Lévy process with no negative jumps. Ann. Probab. 36 (2008) 1777-1789. | MR | Zbl
, and .[3] Lévy Processes. Cambridge Tracts in Mathematics 121. Cambridge Univ. Press, Cambridge, 1996. | MR | Zbl
.[4] Maxima of sums of random variables and suprema of stable processes. Z. Wahrsch. Verw. Gebiete 26 (1973) 273-296. | MR | Zbl
.[5] Invariance principles for random walks conditioned to stay positive. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008) 170-190. | Numdam | MR | Zbl
and .[6] Some explicit identities associated with positive self-similar Markov processes. Stochastic Process. Appl. 119 (2009) 980-1000. | MR | Zbl
, and .[7] The maximum of sums of stable random variables. Trans. Amer. Math. Soc. 83 (1956) 164-169. | MR | Zbl
.[8] On Wiener-Hopf factorisation and the distribution of extrema for certain stable processes. Ann. Probab. 15 (1987) 1352-1362. | MR | Zbl
.[9] On exit time of symmetric α-stable processes. Preprint, 2009.
and .[10] Table of Integrals, Series, and Products, 7th edition. Elsevier/Academic Press, Amsterdam, 2007. | MR | Zbl
and .[11] Wiener-Hopf factorization and distribution of extrema for a family of Lévy processes. J. Appl. Probab. (2009). To appear. | MR
.[12] Introductory Lectures on Fluctuations of Lévy Processes with Applications. Springer, Berlin, 2006. | MR | Zbl
.[13] Fluctuations of spectrally negative Markov additive processes. In Séminaire de probabilités XLI. Lecture Notes in Math. 1934 121-135. Springer, Berlin, 2008. | MR | Zbl
and .[14] Private communication, 2009.
.Cité par Sources :