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References

    Chung, K. L.; Erdös, P. On the application of the Borel-Cantelli lemma. Trans. Amer. Math. Soc. 72, (1952). 179--186. MR0045327 (13,567b)

    Csáki, E.; Erdös, P.; Révész, P. On the length of the longest excursion. Z. Wahrsch. Verw. Gebiete 68 (1985), no. 3, 365--382. MR0771472 (86f:60086)

    Csáki, Endre; Hu, Yueyun. Asymptotic properties of ranked heights in Brownian excursions. J. Theoret. Probab. 14 (2001), no. 1, 77--96. MR1822895 (2002c:60131)

    Csáki, E.; Hu, Y. On the joint asymptotic behaviours of ranked heights of Brownian excursions. Limit theorems in probability and statistics, Vol. I (Balatonlelle, 1999), 347--363, János Bolyai Math. Soc., Budapest, 2002. MR1979973 (2004b:60198)

    Csáki, E.; Hu, Y. On the ranked excursion heights of a Kiefer process. J. Theoret. Probab. 17 (2004), 145--163. Math. Review not available.

    Csáki, Endre; Hu, Yueyun. Lengths and heights of random walk excursions, Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler, (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC (2003), pp. 45--52.

    Csörgö, M.; Révész, P. Strong approximations in probability and statistics. Probability and Mathematical Statistics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. 284 pp. ISBN: 0-12-198540-7 MR0666546 (84d:60050)

    Hu, Yueyun; Shi, Zhan. Extreme lengths in Brownian and Bessel excursions. Bernoulli 3 (1997), no. 4, 387--402. MR1483694 (99c:60169)

    Hu, Yueyun; Shi, Zhan. Shortest excursion lengths. Ann. Inst. H. Poincaré Probab. Statist. 35 (1999), no. 1, 103--120. MR1669912 (99k:60206)

    Knight, Frank B. Essentials of Brownian motion and diffusion. Mathematical Surveys, 18. American Mathematical Society, Providence, R.I., 1981. xiii+201 pp. ISBN: 0-8218-1518-0 MR0613983 (82m:60098)

    Knight, F. B. On the duration of the longest excursion. Seminar on stochastic processes, 1985 (Gainesville, Fla., 1985), 117--147, Progr. Probab. Statist., 12, Birkhäuser Boston, Boston, MA, 1986. MR0896740 (88j:60122)

    Pitman, Jim; Yor, Marc. The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25 (1997), no. 2, 855--900. MR1434129 (98f:60147)

    Pitman, Jim; Yor, Marc. Ranked functionals of Brownian excursions. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 1, 93--97. MR1649517 (99g:60151)

    Pitman, Jim; Yor, Marc. On the distribution of ranked heights of excursions of a Brownian bridge. Ann. Probab. 29 (2001), no. 1, 361--384. MR1825154 (2002b:60139)

    Wendel, J. G. Zero-free intervals of semi-stable Markov processes. Math. Scand. 14 1964 21--34. MR0171319 (30 #1550)



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