Shortest excursion lengths
Hu, Yueyun ; Shi, Zhan
Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999), p. 103-120 / Harvested from Numdam
Publié le : 1999-01-01
@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] R.R. Bahadur, Some Limit Theorems in Statistics. SIAM Publications, Philadelphia, 1971. | MR 315820 | Zbl 0257.62015

[2] J. Bertoin, 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] 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. | MR 57518 | Zbl 0048.11804

[4] M. Chesney, M. Jeanblanc-Picqué and M. Yor, Brownian excursions and Parisian barrier options. Adv. Appl. Probab., Vol. 29, 1997, pp. 165-184. | MR 1432935 | Zbl 0882.60042

[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. | MR 45327 | Zbl 0046.35203

[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. | MR 771472 | Zbl 0537.60062

[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.

[8] Y. Hu and Z. Shi, Extreme lengths in Brownian and Bessel excursions. Bernoulli, Vol. 3, 1997, pp. 387-402. | MR 1483694 | Zbl 0907.60036

[9] S.B. Kochen and C.J. Stone, A note on the Borel-Cantelli lemma. Illinois J. Math., Vol. 8, 1964, pp. 248-251. | MR 161355 | Zbl 0139.35401

[10] J.W. Pitman, Partition structures derived from Brownian motion and stable subordinators. Bernoulli, Vol. 3, 1997, pp. 79-96. | MR 1466546 | Zbl 0882.60081

[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. | MR 1168191 | Zbl 0769.60014

[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. | MR 1434129 | Zbl 0880.60076

[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. | Numdam | MR 1478737 | Zbl 0884.60071

[14] J.W. Pitman and M. Yor, On the relative lengths of excursions derived from a stable subordinator. Ibid, 1997, pp. 287-305. | Numdam | MR 1478738 | Zbl 0884.60072

[15] P. Révész, Random Walk in Random and Non-Random Environments. World Scientific, Singapore, 1990. | Zbl 0733.60091

[16] P. Révész, Long excursions and iterated processes (preprint), 1997 | MR 1661484

[17] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. (Second Edition). Springer, Berlin, 1994. | MR 1303781 | Zbl 0804.60001

[18] C.L. Scheffer, The rank of the present excursion. Stoch. Proc. Appl., Vol. 55, 1995, pp. 101-118. | MR 1312151 | Zbl 0819.60069

[19] A.N. Shiryaev, Probability. (Second Edition). Springer, New York. | MR 1368405