no. 6
On maximum increase and decrease of brownian motion
Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 6, pp. 655-676 
@article{AIHPB_2007__43_6_655_0,
     author = {Salminen, Paavo and Vallois, Pierre},
     title = {On maximum increase and decrease of brownian motion},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {655--676},
     year = {2007},
     publisher = {Elsevier},
     volume = {43},
     number = {6},
     doi = {10.1016/j.anihpb.2006.09.007},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpb.2006.09.007/}
}
TY  - JOUR
AU  - Salminen, Paavo
AU  - Vallois, Pierre
TI  - On maximum increase and decrease of brownian motion
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2007
SP  - 655
EP  - 676
VL  - 43
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpb.2006.09.007/
DO  - 10.1016/j.anihpb.2006.09.007
LA  - en
ID  - AIHPB_2007__43_6_655_0
ER  - 
%0 Journal Article
%A Salminen, Paavo
%A Vallois, Pierre
%T On maximum increase and decrease of brownian motion
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2007
%P 655-676
%V 43
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpb.2006.09.007/
%R 10.1016/j.anihpb.2006.09.007
%G en
%F AIHPB_2007__43_6_655_0
Salminen, Paavo; Vallois, Pierre. On maximum increase and decrease of brownian motion. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 6, pp. 655-676. doi: 10.1016/j.anihpb.2006.09.007

[1] M. Abramowitz, I. Stegun, Mathematical Functions, ninth printing, Dover Publications, New York, 1970.

[2] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, UK, 1996. | Zbl | MR

[3] Ph. Biane, M. Yor, Valeurs principales associées aux temps locaux browniens, Bull. Sci. Math., 2e série 111 (1987) 23-101. | Zbl | MR

[4] A.N. Borodin, P. Salminen, Handbook of Brownian Motion - Facts and Formulae, second ed., Birkhäuser, Basel, 2002. | Zbl

[5] M. Dominé, First passage time distribution of a Wiener process with drift concerning two elastic barriers, J. Appl. Probab. 33 (1996) 164-175. | Zbl | MR

[6] R. Douady, A.N. Shiryayev, M. Yor, On probability characteristics of “downfalls” in a standard Brownian motion, Theory Probab. Appl. 44 (1999) 29-38. | Zbl

[7] J.M. Harrison, Brownian Motion and Stochastic Flow Systems, Wiley, New York, 1985. | Zbl | MR

[8] M. Magdon-Ismail, A.F. Atiya, A. Pratap, Y.S. Abu-Mostafa, On the maximum drawdown of a Brownian motion, J. Appl. Probab. 41 (2004) 147-161. | Zbl | MR

[9] H.P. Mckean, Stochastic Integrals, Academic Press, New York, 1969. | Zbl | MR

[10] J. Pitman, M. Yor, Bessel processes and infinitely divisible laws, in: Williams D. (Ed.), Stochastic Integrals, Springer Lecture Notes in Mathematics, vol. 851, Springer-Verlag, Berlin, 1981, pp. 285-370. | Zbl | MR

[11] J. Pitman, M. Yor, A decomposition of Bessel bridges, Z. Wahrsch. Verw. Gebiete 59 (1982) 425-457. | Zbl | MR

[12] J. Pitman, M. Winkel, Growth of the Brownian forest, Ann. Probab. 33 (6) (2005) 2188-2211. | Zbl | MR

[13] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, third ed., Springer-Verlag, Berlin, 2001. | Zbl

[14] E. Tanré, P. Vallois, Range of Brownian motion with drift, J. Theor. Probab. 19 (1) (2006) 45-69. | Zbl | MR

Cité par Sources :