Moments of last exit times for Lévy processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 2, pp. 207-225. 
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     author = {Sato, Ken-Iti and Watanabe, Toshiro},
     title = {Moments of last exit times for {L\'evy} processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {207--225},
     publisher = {Elsevier},
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     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2003.04.001/}
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Sato, Ken-Iti; Watanabe, Toshiro. Moments of last exit times for Lévy processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 2, pp. 207-225. doi : 10.1016/j.anihpb.2003.04.001. http://www.numdam.org/articles/10.1016/j.anihpb.2003.04.001/

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

[2] R.M. Blumenthal, R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. | MR | Zbl

[3] D.A. Dawson, L.G. Gorostiza, A. Wakolbinger, Occupation time fluctuations in branching systems, J. Theoret. Probab. 14 (2001) 729-796. | MR | Zbl

[4] K.B. Erickson, The strong law of large numbers when the mean is undefined, Trans. Amer. Math. Soc. 185 (1973) 371-381. | MR | Zbl

[5] R.K. Getoor, Some asymptotic formulas involving capacity, Z. Wahrsch. Verw. Gebiete 4 (1965) 248-252. | MR | Zbl

[6] J. Hawkes, Moments of last exit times, Mathematika 24 (1977) 266-269. | MR | Zbl

[7] N. Jain, W.E. Pruitt, The range of random walk, in: Proc. Sixth. Berkeley Symp. Math. Statist. Probab., vol. 3, Univ. Calif. Press, Berkeley, 1972, pp. 31-50. | MR | Zbl

[8] 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. | MR | Zbl

[9] H. Kesten, R.A. Maller, Two renewal theorems for general random walks tending to infinity, Probab. Theory Related Fields 106 (1996) 1-38. | MR | Zbl

[10] K. Petersen, Ergodic Theory, Cambridge Univ. Press, Cambridge, 1983. | MR | Zbl

[11] S.C. Port, Limit theorems involving capacities, J. Math. Mech. 15 (1966) 805-832. | MR | Zbl

[12] S.C. Port, Limit theorems for transient Markov chains, J. Combinatorial Theory 2 (1967) 107-128. | MR | Zbl

[13] S.C. Port, Hitting times for transient stable processes, Pacific J. Math. 21 (1967) 161-165. | MR | Zbl

[14] S.C. Port, C.J. Stone, Infinitely divisible processes and their potential theory, I and II, Ann. Inst. Fourier (Grenoble) 21 (2) (1971) 157-275, and (4) 179-265. | Numdam | Zbl

[15] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, NJ, 1970. | Zbl

[16] K. Sato, Criteria of weak and strong transience for Lévy processes, in: Watanabe S., (Eds.), Probability Theory and Mathematical Statistics, Proc. Seventh Japan-Russia Symp., World Scientific, Singapore, 1996, pp. 438-449. | Zbl

[17] K. Sato, Time evolution of Lévy processes, in: Kono N., Shieh N.R. (Eds.), Trends in Probability and Related Analysis, Proc. SAP '96, World Scientific, Singapore, 1997, pp. 35-82. | MR | Zbl

[18] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge Univ. Press, Cambridge, 1999. | MR | Zbl

[19] M.S. Sgibnev, Asymptotics of infinitely divisible distributions on R, Siberian Math. J. 31 (1990) 115-119. | MR | Zbl

[20] L.A. Shepp, Symmetric random walk, Trans. Amer. Math. Soc. 104 (1962) 144-153. | MR | Zbl

[21] F. Spitzer, Electrostatic capacity, heat flow, and Brownian motion, Z. Wahrsch. Verw. Gebiete 3 (1964) 110-121. | MR | Zbl

[22] J. Takeuchi, Moments of the last exit times, Proc. Japan Acad. 43 (1967) 355-360. | MR | Zbl

[23] J. Takeuchi, T. Yamada, S. Watanabe, Antei katei (Stable processes), in: Seminar on Probability, vol. 13, Kakuritsuron Seminar, Japan, 1962, (in Japanese).

[24] K. Yamamuro, On transient Markov processes of Ornstein-Uhlenbeck type, Nagoya Math. J. 149 (1998) 19-32. | Zbl

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