Spitzer's condition for random walks and Lévy processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 2, pp. 167-178. 
@article{AIHPB_1997__33_2_167_0,
     author = {Bertoin, J. and Doney, R. A.},
     title = {Spitzer's condition for random walks and {L\'evy} processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {167--178},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {2},
     year = {1997},
     mrnumber = {1443955},
     zbl = {0880.60078},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1997__33_2_167_0/}
}
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Bertoin, J.; Doney, R. A. Spitzer's condition for random walks and Lévy processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 2, pp. 167-178. http://www.numdam.org/item/AIHPB_1997__33_2_167_0/

[1] J. Bertoin, Lévy Processes, Cambridge University Press, 1996. | MR | Zbl

[2] J. Bertoin, and M. Yor, Some independence results related to the arc-sine law, J. Theoretic. Prob., Vol. 9, 1996, pp. 447-458. | MR | Zbl

[3] N.H. Bingham, C.M. Goldie, and J.L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987. | MR | Zbl

[4] R.A. Doney, Spitzer's condition and ladder variables in random walk, Probab. Theory Relat. Fields, Vol. 101, 1995, pp. 577-580. | MR | Zbl

[5] W.E. Feller, An Introduction to Probability Theory and its Applications, Vol. 2, 2nd edn. Wiley, New York, 1971.

[6] Fristedt, B.E.: Sample functions of processes with stationary and independent increments. In: Advances in Probability, Vol. 3, 1974, pp. 241-296. | MR | Zbl

[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. | MR | Zbl

[8] F. Spitzer, A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc., Vol. 82, 1956, pp. 323-339. | MR | Zbl

[9] F. Spitzer, Principles of Random Walk, Van Nostrand, Princeton, 1964. | MR | Zbl

[10] C.J. Stone, A local limit theorem for non-lattice multi-dimensional distribution functions, Ann. Math. Stat., Vol. 36, 1965, pp. 546-551. | MR | Zbl