Shortest excursion lengths

Yueyun Hu; Zhan Shi

Annales de l'I.H.P. Probabilités et statistiques (1999)

  • Volume: 35, Issue: 1, page 103-120
  • ISSN: 0246-0203

How to cite


Hu, Yueyun, and Shi, Zhan. "Shortest excursion lengths." Annales de l'I.H.P. Probabilités et statistiques 35.1 (1999): 103-120. <>.

author = {Hu, Yueyun, Shi, Zhan},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {excursion length; Brownian motion},
language = {eng},
number = {1},
pages = {103-120},
publisher = {Gauthier-Villars},
title = {Shortest excursion lengths},
url = {},
volume = {35},
year = {1999},

AU - Hu, Yueyun
AU - Shi, Zhan
TI - Shortest excursion lengths
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1999
PB - Gauthier-Villars
VL - 35
IS - 1
SP - 103
EP - 120
LA - eng
KW - excursion length; Brownian motion
UR -
ER -


  1. [1] R.R. Bahadur, Some Limit Theorems in Statistics. SIAM Publications, Philadelphia, 1971. Zbl0257.62015MR315820
  2. [2] J. Bertoin, Sample path behaviour in connection with generalized arcsine laws. Probab. Th. Rel. Fields, Vol. 103, 1995, pp. 317-327 Zbl0832.60049MR1358080
  3. [3] H. Chernoff, A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Statist., Vol. 23, 1952, pp. 493-507. Zbl0048.11804MR57518
  4. [4] M. Chesney, M. Jeanblanc-Picqué and M. Yor, Brownian excursions and Parisian barrier options. Adv. Appl. Probab., Vol. 29, 1997, pp. 165-184. Zbl0882.60042MR1432935
  5. [5] K.L. Chung and P. Erdos, On the application of the Borel-Cantelli lemma. Trans. Amer. Math. Soc., Vol. 72, 1952, pp. 179-186. Zbl0046.35203MR45327
  6. [6] E. Csáki, P. Erdos and P. Révész, On the length of the longest excursion. Z. Wahrscheinlichkeitstheorie verw. Gebiete, Vol. 68, 1985, pp. 365-382. Zbl0537.60062MR771472
  7. [7] E. Csáki, P. Révész and J. Rosen, Functional laws of the iterated logarithm for local times of recurrent random walks on Z2 (preprint), 1997. Zbl0913.60052
  8. [8] Y. Hu and Z. Shi, Extreme lengths in Brownian and Bessel excursions. Bernoulli, Vol. 3, 1997, pp. 387-402. Zbl0907.60036MR1483694
  9. [9] S.B. Kochen and C.J. Stone, A note on the Borel-Cantelli lemma. Illinois J. Math., Vol. 8, 1964, pp. 248-251. Zbl0139.35401MR161355
  10. [10] J.W. Pitman, Partition structures derived from Brownian motion and stable subordinators. Bernoulli, Vol. 3, 1997, pp. 79-96. Zbl0882.60081MR1466546
  11. [11] J.W. Pitman and M. Yor, Arcsine laws and interval partitions derived from a stable subordinator. Proc. London Math. Soc., Vol. 65, 1992, pp. 326-356. Zbl0769.60014MR1168191
  12. [12] J.W. Pitman and M. Yor, The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab., Vol. 25, 1997, pp. 855-900. Zbl0880.60076MR1434129
  13. [13] J.W. Pitman and M. Yor, On the lengths of excursions of some Markov processes. Sém. Probab. XXXI. Lecture Notes in Mathematics, Vol. 1655, 1997, pp. 272-286, Springer, Berlin. Zbl0884.60071MR1478737
  14. [14] J.W. Pitman and M. Yor, On the relative lengths of excursions derived from a stable subordinator. Ibid, 1997, pp. 287-305. Zbl0884.60072MR1478738
  15. [15] P. Révész, Random Walk in Random and Non-Random Environments. World Scientific, Singapore, 1990. Zbl0733.60091
  16. [16] P. Révész, Long excursions and iterated processes (preprint), 1997 MR1661484
  17. [17] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. (Second Edition). Springer, Berlin, 1994. Zbl0804.60001MR1303781
  18. [18] C.L. Scheffer, The rank of the present excursion. Stoch. Proc. Appl., Vol. 55, 1995, pp. 101-118. Zbl0819.60069MR1312151
  19. [19] A.N. Shiryaev, Probability. (Second Edition). Springer, New York. MR1368405

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