Spitzer's condition for random walks and Lévy processes
Annales de l'I.H.P. Probabilités et statistiques (1997)
- Volume: 33, Issue: 2, page 167-178
- ISSN: 0246-0203
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topBertoin, 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] J. Bertoin, Lévy Processes, Cambridge University Press, 1996. Zbl0861.60003MR1406564
- [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] N.H. Bingham, C.M. Goldie, and J.L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987. Zbl0617.26001MR898871
- [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] W.E. Feller, An Introduction to Probability Theory and its Applications, Vol. 2, 2nd edn. Wiley, New York, 1971. Zbl0219.60003
- [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] 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] F. Spitzer, A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc., Vol. 82, 1956, pp. 323-339. Zbl0071.13003MR79851
- [9] F. Spitzer, Principles of Random Walk, Van Nostrand, Princeton, 1964. Zbl0119.34304MR171290
- [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
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