Spitzer's condition for random walks and Lévy processes

J. Bertoin; R. A. Doney

Annales de l'I.H.P. Probabilités et statistiques (1997)

  • Volume: 33, Issue: 2, page 167-178
  • ISSN: 0246-0203

How to cite

top

Bertoin, J., and Doney, R. A.. "Spitzer's condition for random walks and Lévy processes." Annales de l'I.H.P. Probabilités et statistiques 33.2 (1997): 167-178. <http://eudml.org/doc/77564>.

@article{Bertoin1997,
author = {Bertoin, J., Doney, R. A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {stable laws; ladder variables; arc-sine law; local limit theorems; Wiener-Hopf factorization},
language = {eng},
number = {2},
pages = {167-178},
publisher = {Gauthier-Villars},
title = {Spitzer's condition for random walks and Lévy processes},
url = {http://eudml.org/doc/77564},
volume = {33},
year = {1997},
}

TY - JOUR
AU - Bertoin, J.
AU - Doney, R. A.
TI - Spitzer's condition for random walks and Lévy processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1997
PB - Gauthier-Villars
VL - 33
IS - 2
SP - 167
EP - 178
LA - eng
KW - stable laws; ladder variables; arc-sine law; local limit theorems; Wiener-Hopf factorization
UR - http://eudml.org/doc/77564
ER -

References

top
  1. [1] J. Bertoin, Lévy Processes, Cambridge University Press, 1996. Zbl0861.60003MR1406564
  2. [2] J. Bertoin, and M. Yor, Some independence results related to the arc-sine law, J. Theoretic. Prob., Vol. 9, 1996, pp. 447-458. Zbl0876.60060MR1385407
  3. [3] N.H. Bingham, C.M. Goldie, and J.L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987. Zbl0617.26001MR898871
  4. [4] R.A. Doney, Spitzer's condition and ladder variables in random walk, Probab. Theory Relat. Fields, Vol. 101, 1995, pp. 577-580. Zbl0818.60060MR1327226
  5. [5] W.E. Feller, An Introduction to Probability Theory and its Applications, Vol. 2, 2nd edn. Wiley, New York, 1971. Zbl0219.60003
  6. [6] Fristedt, B.E.: Sample functions of processes with stationary and independent increments. In: Advances in Probability, Vol. 3, 1974, pp. 241-296. Zbl0309.60047MR400406
  7. [7] R.K. Getoor, and M.J. Sharpe, On the arc-sine laws for Lévy processes, J. Appl. Prob., Vol. 31, 1994, pp. 76-89. Zbl0802.60070MR1260572
  8. [8] F. Spitzer, A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc., Vol. 82, 1956, pp. 323-339. Zbl0071.13003MR79851
  9. [9] F. Spitzer, Principles of Random Walk, Van Nostrand, Princeton, 1964. Zbl0119.34304MR171290
  10. [10] C.J. Stone, A local limit theorem for non-lattice multi-dimensional distribution functions, Ann. Math. Stat., Vol. 36, 1965, pp. 546-551. Zbl0135.19204MR175166

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.