Spitzer's condition for random walks and Lévy processes

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 33, Issue 2, 1997, Pages 167-178

  Bertoin, J ^a   Doney, R A ^b  

^a University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Arc sine law; Ladder variables; Local limit theorems; Stable laws; Wiener Hopf factorisation

Indexed keywords

EID: 0031537025     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(97)80120-3     Document Type: Article

References (10)

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3. [3] N. H. BINGHAM, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.
4. [4] R. A. DONEY, Spitzer's condition and ladder variables in random walk, Probab. Theory Relat. Fields, Vol. 101, 1995, pp. 577-580.
5. [5] W. E. FELLER, An Introduction to Probability Theory and its Applications, Vol. 2, 2nd edn. Wiley, New York, 1971.
6. [6] FRISTEDT, B.E.: Sample functions of processes with stationary and independent increments. In: Advances in Probability, Vol. 3, 1974, pp. 241-296.
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.
8. [8] F. SPITZER, A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc., Vol. 82, 1956, pp. 323-339.
9. [9] F. SPITZER, Principles of Random Walk, Van Nostrand, Princeton, 1964.
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.