Extreme lengths in Brownian and Bessel excursions

Bernoulli

Volumn 3, Issue 4, 1997, Pages 387-402

  Hu, Yueyun ^a   Shi, Zhan ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Bessel process; Brownian motion; Excursion length; L vy's class

Indexed keywords

EID: 0009048612     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318455     Document Type: Article

References (19)

1. Bertoin, J. (1995) Sample path behaviour in connection with generalized arcsine laws. Probab. Theory Related Fields, 103, 317-327.
2. Chesney, M., Jeanblanc-PicqueÂ, M. and Yor, M (1997) Brownian excursions and Parisian options. Adv. Appl. Probab., 29, 165-184.
3. Chung, K.L. and Erdös, P. (1952) On the application of the Borel-Cantelli lemma. Trans. Amer. Math. Soc., 72, 179-186.
4. Csáki, E., ErdoÈ s, P. and ReÂveÂsz, P. (1985) On the length of the longest excursion. Z. Wahrscheinlichkeitstheorie Verw. Geb., 68, 365-382.
5. Erdös, P. (1942) On the law of the iterated logarithm. Ann. Math., 43, 419-436.
6. Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. II (2nd edn). New York: Wiley.
7. Hobson, D.G. (1992) Topics in the long-time behaviour of diffusions. PhD thesis, University of Cambridge.
8. Hobson, D.G. (1994) Asymptotics for an arcsin type result. Ann. Inst. H. Poincare Probab. Statist., 30, 235-243.
9. Jeulin, T. (1980) Semi-martingales et Grossissement d'une Filtration, Lecture Notes in Math. 833. Berlin: Springer-Verlag.
10. Knight, F.B. (1986) On the duration of the longest excursion. In E. CË inlar, K.L. Chung and M.J. Sharpe (eds), Seminar on Stochastic Processes 1985, Progr. Probab. Statist. 12, pp. 117-147. Boston: BirkhaÈuser.
11. Kochen, S.B. and Stone, C.J. (1964) A note on the Borel-Cantelli lemma. Illinois J. Math., 8, 248-251.
12. Molchanov, S.A. and Ostrovski, E. (1969) Symmetric stable processes as traces of degenerate diffusions. Theory Probab. Appl., 14, 128-131.
13. Perman, M. (1993) Order statistics for jumps of normalised subordinators. Stoch. Process. Appl., 46, 267-281.
14. Perman, M., Pitman, J.W. and Yor, M. (1992) Size-biased sampling of Poisson point processes and excursions. Probab. Theory Related Fields, 92, 21-39.
15. Pitman, J.W. and Yor, M. (1992) Arcsine laws and interval partitions derived from a stable subordinator. Proc. London Math. Soc. (3), 65, 326-356.
16. Pitman, J.W. and Yor, M. (1997) The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. To appear.
17. Revuz, D. and Yor, M. (1994) Continuous Martingales and Brownian Motion (2nd edn). Berlin: Springer-Verlag.
18. Tenenbaum, G. (1995) Introduction to Analytic and Probabilistic Number Theory. Cambridge: Cambridge University Press.
19. Yor, M. (1995) Local Times and Excursions for Brownian Motion: A Concise Introduction. Lecciones Mat., Universidad Central de Venezuela.