Last exit times for transient semistable processes
Sato, Ken-Iti ; Watanabe, Toshiro
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005), p. 929-951 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2005__41_5_929_0,
     author = {Sato, Ken-Iti and Watanabe, Toshiro},
     title = {Last exit times for transient semistable processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {41},
     year = {2005},
     pages = {929-951},
     doi = {10.1016/j.anihpb.2004.09.003},
     mrnumber = {2165258},
     zbl = {1086.60028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_5_929_0}
}

Sato, Ken-Iti; Watanabe, Toshiro. Last exit times for transient semistable processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) pp. 929-951. doi : 10.1016/j.anihpb.2004.09.003. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_5_929_0/

[1] J. Bertoin, Lévy Processes, Cambridge University 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] G.S. Choi, Criteria for recurrence and transience of semistable processes, Nagoya Math. J. 134 (1994) 91-106. | MR 1280655 | Zbl 0804.60064

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

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

[6] S. Hiraba, Asymptotic behaviour of densities of multi-dimensional stable distributions, Tsukuba J. Math. 18 (1994) 223-246. | MR 1287843 | Zbl 0807.60021

[7] N. Jain, W.E. Pruitt, The range of random walk, in: Proc. Sixth Berkeley Symp. Math. Statist. Probab., vol. 3, University of California Press, Berkeley and Los Angeles, 1972, pp. 31-50. | MR 410936 | Zbl 0276.60066

[8] J.-F. Le Gall, Sur une conjecture de M. Kac, Probab. Theory Related Fields 78 (1988) 389-402. | MR 949180 | Zbl 0655.60067

[9] P. Lévy, Théorie de l'Addition des Variables Aléatoires, Gauthier-Villars, Paris, 1937, 2e éd., 1954. | JFM 63.0490.04

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

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

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

[13] S.C. Port, Stable processes with drift on the line, Trans. Amer. Math. Soc. 313 (1989) 605-841. | MR 997680 | Zbl 0681.60068

[14] S.C. Port, Asymptotic expansions for the expected volume of a stable sausage, Ann. Probab. 18 (1990) 492-523. | MR 1055417 | Zbl 0705.60061

[15] S.C. Port, Spitzer's formula involving capacity, in: Durrett R., Kesten H. (Eds.), Random Walks, Brownian Motion, and Interacting Particle Systems. A Festschrift in Honor of Frank Spitzer, Birkhäuser, Boston, 1991, pp. 373-388. | MR 1146459 | Zbl 0737.60013

[16] 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. | Numdam | Numdam | MR 346919 | Zbl 0195.47601

[17] S.C. Port, R.A. Vitale, Positivity of stable densities, Proc. Amer. Math. Soc. 102 (1988) 1018-1023. | MR 934885 | Zbl 0648.60016

[18] B.S. Rajput, K. Rama-Murthy, T. Zak, Supports of semi-stable probability measures on locally convex spaces, J. Theor. Probab. 7 (1994) 931-942. | MR 1295546 | Zbl 0807.60005

[19] K. Sato, Time evolution in distributions of Lévy processes, Southeast Asian Bull. Math. 19 (2) (1995) 17-26. | MR 1376625 | Zbl 0843.60066

[20] 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. | MR 1467961 | Zbl 0963.60043

[21] 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

[22] K. Sato, Semi-stable processes and their extensions, in: Kono N., Shieh N.-R. (Eds.), Trends in Probability and Related Analysis, Proc. SAP '98, World Scientific, Singapore, 1999, pp. 129-145. | MR 1819201 | Zbl 01665464

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

[24] K. Sato, T. Watanabe, Moments of last exit times for Lévy processes, Ann. Inst. H. Poincaré Probab. Statist. 40 (2004) 207-225. | Numdam | MR 2044816 | Zbl 1053.60048

[25] M.J. Sharpe, Supports of convolution semigroups and densities, in: Probability Measures on Groups and Related Structures, XI (Oberwolfach, 1994), World Scientific, River Edge, NJ, 1995, pp. 364-369. | MR 1414946 | Zbl 0909.60052

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

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

[28] S.J. Taylor, Sample path properties of a transient stable process, J. Math. Mech. 16 (1967) 1229-1246. | MR 208684 | Zbl 0178.19301

[29] A. Tortrat, Le support des lois indéfiniment divisibles dans un groupe Abélien localemnet compact, Math. Z. 197 (1988) 231-250. | MR 923491 | Zbl 0618.60013

[30] T. Watanabe, Oscillation of modes of some semi-stable Lévy processes, Nagoya Math. J. 132 (1993) 141-153. | MR 1253699 | Zbl 0816.60016

[31] T. Watanabe, Some examples on unimodality of Lévy processes, Kodai Math. J. 17 (1994) 38-47. | MR 1262952 | Zbl 0803.60072