Moments of last exit times for Lévy processes
Sato, Ken-Iti ; Watanabe, Toshiro
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004), p. 207-225 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2004__40_2_207_0,
     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},
     volume = {40},
     year = {2004},
     pages = {207-225},
     doi = {10.1016/j.anihpb.2003.04.001},
     mrnumber = {2044816},
     zbl = {1053.60048},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2004__40_2_207_0}
}

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) pp. 207-225. doi : 10.1016/j.anihpb.2003.04.001. http://gdmltest.u-ga.fr/item/AIHPB_2004__40_2_207_0/

[1] J. Bertoin, Lévy Processes, Cambridge Univ. Press, Cambridge, 1996. | MR 1406564 | Zbl 0861.60003

[2] R.M. Blumenthal, R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. | MR 264757 | Zbl 0169.49204

[3] D.A. Dawson, L.G. Gorostiza, A. Wakolbinger, Occupation time fluctuations in branching systems, J. Theoret. Probab. 14 (2001) 729-796. | MR 1860521 | Zbl 0991.60095

[4] K.B. Erickson, The strong law of large numbers when the mean is undefined, Trans. Amer. Math. Soc. 185 (1973) 371-381. | MR 336806 | Zbl 0304.60016

[5] R.K. Getoor, Some asymptotic formulas involving capacity, Z. Wahrsch. Verw. Gebiete 4 (1965) 248-252. | MR 190988 | Zbl 0295.60055

[6] J. Hawkes, Moments of last exit times, Mathematika 24 (1977) 266-269. | MR 488316 | Zbl 0384.60053

[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 410936 | Zbl 0276.60066

[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 867090 | Zbl 0612.60060

[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 1408415 | Zbl 0855.60080

[10] K. Petersen, Ergodic Theory, Cambridge Univ. Press, Cambridge, 1983. | MR 833286 | Zbl 0507.28010

[11] S.C. Port, Limit theorems involving capacities, J. Math. Mech. 15 (1966) 805-832. | MR 211471 | Zbl 0146.38406

[12] S.C. Port, Limit theorems for transient Markov chains, J. Combinatorial Theory 2 (1967) 107-128. | MR 207046 | Zbl 0162.49101

[13] S.C. Port, Hitting times for transient stable processes, Pacific J. Math. 21 (1967) 161-165. | MR 208681 | Zbl 0154.18904

[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 | Numdam | Zbl 0195.47601

[15] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, NJ, 1970. | Zbl 0193.18401

[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 0963.60043

[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 1616274 | Zbl 1010.60042

[18] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge Univ. Press, Cambridge, 1999. | MR 1739520 | Zbl 0973.60001

[19] M.S. Sgibnev, Asymptotics of infinitely divisible distributions on R, Siberian Math. J. 31 (1990) 115-119. | MR 1046818 | Zbl 0714.60010

[20] L.A. Shepp, Symmetric random walk, Trans. Amer. Math. Soc. 104 (1962) 144-153. | MR 139212 | Zbl 0201.50102

[21] F. Spitzer, Electrostatic capacity, heat flow, and Brownian motion, Z. Wahrsch. Verw. Gebiete 3 (1964) 110-121. | MR 172343 | Zbl 0126.33505

[22] J. Takeuchi, Moments of the last exit times, Proc. Japan Acad. 43 (1967) 355-360. | MR 222961 | Zbl 0178.19403

[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 0908.60074