@article{AIHPB_1999__35_1_103_0,
author = {Hu, Yueyun and Shi, Zhan},
title = {Shortest excursion lengths},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
volume = {35},
year = {1999},
pages = {103-120},
mrnumber = {1669912},
zbl = {0921.60073},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPB_1999__35_1_103_0}
}
Hu, Yueyun; Shi, Zhan. Shortest excursion lengths. Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) pp. 103-120. http://gdmltest.u-ga.fr/item/AIHPB_1999__35_1_103_0/
[1] , Some Limit Theorems in Statistics. SIAM Publications, Philadelphia, 1971. | MR 315820 | Zbl 0257.62015
[2] , Sample path behaviour in connection with generalized arcsine laws. Probab. Th. Rel. Fields, Vol. 103, 1995, pp. 317-327 | MR 1358080 | Zbl 0832.60049
[3] , 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. | MR 57518 | Zbl 0048.11804
[4] , and , Brownian excursions and Parisian barrier options. Adv. Appl. Probab., Vol. 29, 1997, pp. 165-184. | MR 1432935 | Zbl 0882.60042
[5] and , On the application of the Borel-Cantelli lemma. Trans. Amer. Math. Soc., Vol. 72, 1952, pp. 179-186. | MR 45327 | Zbl 0046.35203
[6] , and , On the length of the longest excursion. Z. Wahrscheinlichkeitstheorie verw. Gebiete, Vol. 68, 1985, pp. 365-382. | MR 771472 | Zbl 0537.60062
[7] , and , Functional laws of the iterated logarithm for local times of recurrent random walks on Z2 (preprint), 1997.
[8] and , Extreme lengths in Brownian and Bessel excursions. Bernoulli, Vol. 3, 1997, pp. 387-402. | MR 1483694 | Zbl 0907.60036
[9] and , A note on the Borel-Cantelli lemma. Illinois J. Math., Vol. 8, 1964, pp. 248-251. | MR 161355 | Zbl 0139.35401
[10] , Partition structures derived from Brownian motion and stable subordinators. Bernoulli, Vol. 3, 1997, pp. 79-96. | MR 1466546 | Zbl 0882.60081
[11] and , Arcsine laws and interval partitions derived from a stable subordinator. Proc. London Math. Soc., Vol. 65, 1992, pp. 326-356. | MR 1168191 | Zbl 0769.60014
[12] and , The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab., Vol. 25, 1997, pp. 855-900. | MR 1434129 | Zbl 0880.60076
[13] and , On the lengths of excursions of some Markov processes. Sém. Probab. XXXI. Lecture Notes in Mathematics, Vol. 1655, 1997, pp. 272-286, Springer, Berlin. | Numdam | MR 1478737 | Zbl 0884.60071
[14] and , On the relative lengths of excursions derived from a stable subordinator. Ibid, 1997, pp. 287-305. | Numdam | MR 1478738 | Zbl 0884.60072
[15] , Random Walk in Random and Non-Random Environments. World Scientific, Singapore, 1990. | Zbl 0733.60091
[16] , Long excursions and iterated processes (preprint), 1997 | MR 1661484
[17] and , Continuous Martingales and Brownian Motion. (Second Edition). Springer, Berlin, 1994. | MR 1303781 | Zbl 0804.60001
[18] , The rank of the present excursion. Stoch. Proc. Appl., Vol. 55, 1995, pp. 101-118. | MR 1312151 | Zbl 0819.60069
[19] , Probability. (Second Edition). Springer, New York. | MR 1368405