Sinaǐ's condition for real valued Lévy processes

Rivero, Víctor

doi:10.1016/j.anihpb.2006.03.004

Rivero, Víctor

Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 3, pp. 299-319.

Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpb.2006.03.004

@article{AIHPB_2007__43_3_299_0,
     author = {Rivero, V{\'\i}ctor},
     title = {Sinaǐ's condition for real valued {L\'evy} processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {299--319},
     publisher = {Elsevier},
     volume = {43},
     number = {3},
     year = {2007},
     doi = {10.1016/j.anihpb.2006.03.004},
     zbl = {1115.60049},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2006.03.004/}
}

TY  - JOUR
AU  - Rivero, Víctor
TI  - Sinaǐ's condition for real valued Lévy processes
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2007
SP  - 299
EP  - 319
VL  - 43
IS  - 3
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpb.2006.03.004/
DO  - 10.1016/j.anihpb.2006.03.004
LA  - en
ID  - AIHPB_2007__43_3_299_0
ER  -

%0 Journal Article
%A Rivero, Víctor
%T Sinaǐ's condition for real valued Lévy processes
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2007
%P 299-319
%V 43
%N 3
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpb.2006.03.004/
%R 10.1016/j.anihpb.2006.03.004
%G en
%F AIHPB_2007__43_3_299_0

Rivero, Víctor. Sinaǐ's condition for real valued Lévy processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 3, pp. 299-319. doi : 10.1016/j.anihpb.2006.03.004. http://archive.numdam.org/articles/10.1016/j.anihpb.2006.03.004/

Bibliographie
Cité par

[1] S. Asmussen, V. Kalashnikov, D. Konstantinides, C. Klüppelberg, G. Tsitsiashvili, A local limit theorem for random walk maxima with heavy tails, Statist. Probab. Lett. 56 (4) (2002) 399-404. | MR | Zbl

[2] J. Bertoin, Lévy Processes, Cambridge Tracts in Mathematics, vol. 121, Cambridge University Press, Cambridge, 1996. | MR | Zbl

[3] J. Bertoin, R.A. Doney, Cramér's estimate for Lévy processes, Statist. Probab. Lett. 21 (5) (1994) 363-365. | MR | Zbl

[4] N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, Encyclopedia of Mathematics and its Applications, vol. 27, Cambridge University Press, Cambridge, 1989. | MR | Zbl

[5] Y.S. Chow, On moments of ladder height variables, Adv. Appl. Math. 7 (1) (1986) 46-54. | MR | Zbl

[6] F. De Weert, Attraction to stable distributions for Lévy processes at zero, Technical report, University of Manchester, 2003.

[7] R. Doney, Fluctuation theory for Lévy processes, in: Lévy Processes, Birkhäuser Boston, Boston, MA, 2001, pp. 57-66. | MR | Zbl

[8] R.A. Doney, R.A. Maller, Stability of the overshoot for Lévy processes, Ann. Probab. 30 (1) (2002) 188-212. | MR | Zbl

[9] E.B. Dynkin, Some limit theorems for sums of independent random quantities with infinite mathematical expectations, Izv. Akad. Nauk SSSR Ser. Mat. 19 (1955) 247-266. | MR | Zbl

[10] K.B. Erickson, The strong law of large numbers when the mean is undefined, Trans. Amer. Math. Soc. 185 (1973) 371-381, (1974). | MR | Zbl

[11] B. Fristedt, Sample functions of stochastic processes with stationary, independent increments, in: Advances in Probability and Related Topics, vol. 3, Dekker, New York, 1974, pp. 241-396. | MR | Zbl

[12] B.E. Fristedt, W.E. Pruitt, Lower functions for increasing random walks and subordinators, Z. Wahrsch. Verw. Gebiete 18 (1971) 167-182. | MR | Zbl

[13] J.L. Geluk, L. De Haan, Regular Variation, Extensions and Tauberian Theorems, CWI Tract, vol. 40, Stichting Mathematisch Centrum voor Wiskunde en Informatica, Amsterdam, 1987. | MR | Zbl

[14] I˘.Ī. Gīhman, A.V. Skorohod, The Theory of Stochastic Processes. II, Die Grundlehren der Mathematischen Wissenschaften, vol. 218, Springer-Verlag, New York, 1975, Translated from the Russian by Samuel Kotz. | MR | Zbl

[15] P. Greenwood, E. Omey, J.L. Teugels, Harmonic renewal measures, Z. Wahrsch. Verw. Gebiete 59 (3) (1982) 391-409. | MR | Zbl

[16] R. Grübel, Tail behaviour of ladder-height distributions in random walks, J. Appl. Probab. 22 (3) (1985) 705-709. | MR | Zbl

[17] H. Kesten, The limit points of a normalized random walk, Ann. Math. Statist. 41 (1970) 1173-1205. | MR | Zbl

[18] C. Klüppelberg, Subexponential distributions and integrated tails, J. Appl. Probab. 25 (1) (1988) 132-141. | MR | Zbl

[19] C. Klüppelberg, A.E. Kyprianou, R.A. Maller, Ruin probabilities and overshoots for general Lévy insurance risk processes, Ann. Appl. Probab. 14 (4) (2004) 1766-1801. | MR | Zbl

[20] B.A. Rogozin, Distribution of the first ladder moment and height, and fluctuations of a random walk, Teor. Verojatnost. i Primenen. 16 (1971) 539-613. | MR | Zbl

[21] K.-I. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge Studies in Advanced Mathematics, vol. 68, Cambridge University Press, Cambridge, 1999. | MR | Zbl

[22] N. Veraverbeke, Asymptotic behaviour of Wiener-Hopf factors of a random walk, Stochastic Processes Appl. 5 (1) (1977) 27-37. | Zbl

[23] V. Vigon, Simplifiez vos Lévy en titillant la factorisation de Wiener-Hopf, PhD thesis, Université Louis Pasteur, 2002.

[24] V. Vigon, Votre Lévy rampe-t-il ?, J. London Math. Soc. (2) 65 (1) (2002) 243-256. | MR | Zbl

Cité par Sources :