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Invariance Principles for Ranked Excursion Lengths and Heights
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Endre Csáki, A. Rényi Institute of Mathematics, Hungarian Academy of Sciences
Yueyun Hu, Universite Paris VI
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Abstract
In this note we prove strong invariance principles between
ranked excursion lengths and heights of a simple random walk and those of
a standard Brownian motion. Some consequences concerning limiting
distributions and strong limit theorems will also be presented.
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Full text: PDF
Pages: 14-21
Published on: February 18, 2004
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Bibliography
| 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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Electronic Communications in Probability. ISSN: 1083-589X |
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