On the relative lengths of excursions derived from a stable subordinator
Séminaire de probabilités de Strasbourg, Tome 31 (1997), pp. 287-305. 
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     author = {Pitman, Jim and Yor, Marc},
     title = {On the relative lengths of excursions derived from a stable subordinator},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {287--305},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {31},
     year = {1997},
     mrnumber = {1478738},
     zbl = {0884.60072},
     language = {en},
     url = {http://www.numdam.org/item/SPS_1997__31__287_0/}
}
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Pitman, Jim; Yor, Marc. On the relative lengths of excursions derived from a stable subordinator. Séminaire de probabilités de Strasbourg, Tome 31 (1997), pp. 287-305. http://www.numdam.org/item/SPS_1997__31__287_0/

[1] M. Barlow. Skew brownian motion and a one-dimensional differential equation. Stochastics, 25:1-2, 1988. | MR | Zbl

[2] M. Barlow, J. Pitman, and M. Yor. Une extension multidimensionnelle de la loi de l'arc sinus. In Séminaire de Probabilités XXIII, pages 294-314. Springer, 1989. Lecture Notes in Math. 1372. | Numdam | MR | Zbl

[3] E.B. Dynkin. Some limit theorems for sums of independent random variables with infinite mathematical expectations. IMS-AMS Selected Translations in Math. Stat. and Prob., 1:171-189, 1961. | MR | Zbl

[4] B. Fristedt and S.J. Taylor. Constructions of local time for a Markov process. Z. Wahrsch. Verw. Gebiete, 62:73 - 112, 1983. | MR | Zbl

[5] P. Greenwood and J. Pitman. Construction of local time and Poisson point processes from nested arrays. Journal of the London Mathematical Society, 22:182-192, 1980. | MR | Zbl

[6] J.M. Harrison and L.A. Shepp. On skew Brownian motion. The Annals of Probability, 9:309 - 313, 1981. | MR | Zbl

[7] J.F.C. Kingman. Random discrete distributions. J. Roy. Statist. Soc. B, 37:1-22, 1975. | MR | Zbl

[8] F.B. Knight. On the duration of the longest excursion. In E. Cinlar, K.L. Chung, and R.K. Getoor, editors, Seminar on Stochastic Processes, pages 117-148. Birkhäuser, 1985. | MR | Zbl

[9] J. Lamperti. An occupation time theorem for a class of stochastic processes. Trans. Amer. Math. Soc., 88:380 - 387, 1958. | MR | Zbl

[10] J. Lamperti. An invariance principle in renewal theory. Ann. Math. Stat., 33:685 - 696, 1962. | MR | Zbl

[11] P. Lévy. Sur certains processus stochastiques homogènes. Compositio Math., 7:283-339, 1939. | JFM | Numdam | MR | Zbl

[12] M. Perman. Order statistics for jumps of normalized subordinators. Stoch. Proc. Appl., 46:267-281, 1993. | MR | Zbl

[13] M. Perman, J. Pitman, and M. Yor. Size-biased sampling of Poisson point processes and excursions. Probability Theory and Related Fields, 92:21-39, 1992. | MR | Zbl

[14] J. Pitman. Partition structures derived from Brownian motion and stable subordinators. Technical Report 346, Dept. Statistics, U.C. Berkeley, 1992. To appear in Bernoulli. | MR | Zbl

[15] J. Pitman and M. Yor. Arcsine laws and interval partitions derived from a stable subordinator. Proc. London Math. Soc. (3), 65:326-356, 1992. | MR | Zbl

[16] J. Pitman and M. Yor. The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Technical Report 433, Dept. Statistics, U.C. Berkeley, 1995. To appear in The Annals of Probability. | MR | Zbl

[17] J. Pitman and M. Yor. Random discrete distributions derived from self-similar random sets. Electronic J. Probability, 1:Paper 4, 1-28, 1996. | MR | Zbl

[18] J. Pitman and M. Yor. Some conditional expectations given an average of a stationary or self-similar random process. Technical Report 438, Dept. Statistics, U.C. Berkeley, 1996. In preparation.

[19] C.L. Scheffer. The rank of the present excursion. Stoch. Proc. Appl., 55:101-118, 1995. | MR | Zbl

[20] M.S. Taqqu. A bibliographical guide to self-similar processes and long-range dependence. In Dependence in Probab. and Stat.: A Survey of Recent Results; Ernst Eberlein, Murad S. Taqqu (Ed.), pages 137-162. Birkhäuser (Basel, Boston), 1986. | MR | Zbl

[21] J. Walsh. A diffusion with a discontinuous local time. In Temps Locaux, volume 52-53 of Astérisque, pages 37-45. Soc. Math. de France, 1978.

[22] S. Watanabe. On time inversion of one-dimensional diffusion processes. Z. Wahrsch. Verw. Gebiete, 31:115-124, 1975. | MR | Zbl

[23] S. Watanabe. Generalized arc-sine laws for one-dimensional diffusion processes and random walks. In Proceedings of Symposia in Pure Mathematics, volume 57, pages 157-172. A.M.S., 1995. | MR | Zbl

[24] J.G. Wendel. Zero-free intervals of semi-stable Markov processes. Math. Scand., 14:21 - 34, 1964. | MR | Zbl

[25] M. Yor. Some Aspects of Brownian Motion. Lectures in Math., ETH Zürich. Birkhaüser, 1992. Part I: Some Special Functionals. | MR | Zbl

[26] M. Yor. Random Brownian scaling and some absolute continuity relationships. In E. Bolthausen, M. Dozzi, and F. Russo, editors, Seminar on Stochastic Analysis, Random Fields and Applications. Centro Stefano Franscini, Ascona, 1993, pages 243-252. Birkhäuser, 1995. | MR | Zbl