Moments of passage times for Lévy processes

R. A. Doney; R. A. Maller

Annales de l'I.H.P. Probabilités et statistiques (2004)

  • Volume: 40, Issue: 3, page 279-297
  • ISSN: 0246-0203

How to cite

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Doney, R. A., and Maller, R. A.. "Moments of passage times for Lévy processes." Annales de l'I.H.P. Probabilités et statistiques 40.3 (2004): 279-297. <http://eudml.org/doc/77811>.

@article{Doney2004,
author = {Doney, R. A., Maller, R. A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Passage times of Lévy processes; Horizontal boundaries; Curved boundaries; Drift to infinity; Renewal theorems; Local time; Ladder height processes; Strong laws},
language = {eng},
number = {3},
pages = {279-297},
publisher = {Elsevier},
title = {Moments of passage times for Lévy processes},
url = {http://eudml.org/doc/77811},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Doney, R. A.
AU - Maller, R. A.
TI - Moments of passage times for Lévy processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2004
PB - Elsevier
VL - 40
IS - 3
SP - 279
EP - 297
LA - eng
KW - Passage times of Lévy processes; Horizontal boundaries; Curved boundaries; Drift to infinity; Renewal theorems; Local time; Ladder height processes; Strong laws
UR - http://eudml.org/doc/77811
ER -

References

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  1. [1] J. Bertoin, An Introduction to Lévy Processes, Cambridge University Press, Cambridge, 1996. Zbl0861.60003MR1406564
  2. [2] N.H. Bingham, R.A. Doney, Asymptotic properties of super-critical branching processes, I: The Galton–Watson process, Adv. Appl. Probab.6 (1975) 711-731. Zbl0297.60044
  3. [3] N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987. Zbl0617.26001MR898871
  4. [4] R.A. Doney, Stochastic bounds for Lévy processes, Ann. Probab., in press. Zbl1046.60045MR2060308
  5. [5] R.A. Doney, R.A. Maller, Stability and attraction to normality for Lévy processes at zero and infinity, J. Theoret. Probab.15 (2002) 751-792. Zbl1015.60043MR1922446
  6. [6] K.B. Erickson, The strong law of large numbers when the mean is undefined, Trans. Amer. Math. Soc.185 (1973) 371-381. Zbl0304.60016MR336806
  7. [7] S. Janson, Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift, Adv. Appl. Probab.18 (1986) 865-879. Zbl0612.60060MR867090
  8. [8] H. Kesten, R.A. Maller, Two renewal theorems for general random walks tending to infinity, Probab. Theory Related Fields106 (1996) 1-38. Zbl0855.60080MR1408415
  9. [9] W.E. Pruitt, General one-sided laws of the iterated logarithm, Ann. Probab.9 (1981) 1-48. Zbl0462.60030MR606797
  10. [10] B.A. Rogozin, Local behaviour of processes with independent increments, Theor. Probab. Appl.13 (1968) 482-486. Zbl0177.21305MR242261
  11. [11] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, 1999. Zbl0973.60001MR1739520
  12. [12] V. Vigon, Votre Lévy ramp-t-il?, J. London Math. Soc.65 (2002) 243-256. Zbl1016.60054MR1875147

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