Last exit times for transient semistable processes

 Access to full text

 Full (PDF)

1. [1] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1996. Zbl0861.60003MR1406564
2. [2] R.M. Blumenthal, R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. Zbl0169.49204MR264757
3. [3] G.S. Choi, Criteria for recurrence and transience of semistable processes, Nagoya Math. J.134 (1994) 91-106. Zbl0804.60064MR1280655
4. [4] R.K. Getoor, Some asymptotic formulas involving capacity, Z. Wahrsch. Verw. Gebiete4 (1965) 248-252. Zbl0295.60055MR190988
5. [5] J. Hawkes, Moments of last exit times, Mathematika24 (1977) 266-269. Zbl0384.60053MR488316
6. [6] S. Hiraba, Asymptotic behaviour of densities of multi-dimensional stable distributions, Tsukuba J. Math.18 (1994) 223-246. Zbl0807.60021MR1287843
7. [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. Zbl0276.60066MR410936
8. [8] J.-F. Le Gall, Sur une conjecture de M. Kac, Probab. Theory Related Fields78 (1988) 389-402. Zbl0655.60067MR949180
9. [9] P. Lévy, Théorie de l'Addition des Variables Aléatoires, Gauthier-Villars, Paris, 1937, 2e éd., 1954. Zbl63.0490.04JFM63.0490.04
10. [10] S.C. Port, Limit theorems involving capacities, J. Math. Mech.15 (1966) 805-832. Zbl0146.38406MR211471
11. [11] S.C. Port, Limit theorems for transient Markov chains, J. Combin. Theory2 (1967) 107-128. Zbl0162.49101MR207046
12. [12] S.C. Port, Hitting times for transient stable processes, Pacific J. Math.21 (1967) 161-165. Zbl0154.18904MR208681
13. [13] S.C. Port, Stable processes with drift on the line, Trans. Amer. Math. Soc.313 (1989) 605-841. Zbl0681.60068MR997680
14. [14] S.C. Port, Asymptotic expansions for the expected volume of a stable sausage, Ann. Probab.18 (1990) 492-523. Zbl0705.60061MR1055417
15. [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. Zbl0737.60013MR1146459
16. [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. Zbl0195.47601MR346919
17. [17] S.C. Port, R.A. Vitale, Positivity of stable densities, Proc. Amer. Math. Soc.102 (1988) 1018-1023. Zbl0648.60016MR934885
18. [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. Zbl0807.60005MR1295546
19. [19] K. Sato, Time evolution in distributions of Lévy processes, Southeast Asian Bull. Math.19 (2) (1995) 17-26. Zbl0843.60066MR1376625
20. [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. Zbl0963.60043MR1467961
21. [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. Zbl1010.60042MR1616274
22. [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. Zbl1171.60345MR1819201
23. [23] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, 1999. Zbl0973.60001MR1739520
24. [24] K. Sato, T. Watanabe, Moments of last exit times for Lévy processes, Ann. Inst. H. Poincaré Probab. Statist.40 (2004) 207-225. Zbl1053.60048MR2044816
25. [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. Zbl0909.60052MR1414946
26. [26] F. Spitzer, Electrostatic capacity, heat flow, and Brownian motion, Z. Wahrsch. Verw. Gebiete3 (1964) 110-121. Zbl0126.33505MR172343
27. [27] J. Takeuchi, Moments of the last exit times, Proc. Japan Acad.43 (1967) 355-360. Zbl0178.19403MR222961
28. [28] S.J. Taylor, Sample path properties of a transient stable process, J. Math. Mech.16 (1967) 1229-1246. Zbl0178.19301MR208684
29. [29] A. Tortrat, Le support des lois indéfiniment divisibles dans un groupe Abélien localemnet compact, Math. Z.197 (1988) 231-250. Zbl0618.60013MR923491
30. [30] T. Watanabe, Oscillation of modes of some semi-stable Lévy processes, Nagoya Math. J.132 (1993) 141-153. Zbl0816.60016MR1253699
31. [31] T. Watanabe, Some examples on unimodality of Lévy processes, Kodai Math. J.17 (1994) 38-47. Zbl0803.60072MR1262952