On maximum increase and decrease of brownian motion
Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 6, p. 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},
     publisher = {Elsevier},
     volume = {43},
     number = {6},
     year = {2007},
     pages = {655-676},
     doi = {10.1016/j.anihpb.2006.09.007},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 43 (2007) no. 6, pp. 655-676. doi : 10.1016/j.anihpb.2006.09.007. http://www.numdam.org/item/AIHPB_2007__43_6_655_0/

[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. | MR 1406564 | Zbl 0861.60003

[3] Ph. Biane, M. Yor, Valeurs principales associées aux temps locaux browniens, Bull. Sci. Math., 2e série 111 (1987) 23-101. | MR 886959 | Zbl 0619.60072

[4] A.N. Borodin, P. Salminen, Handbook of Brownian Motion - Facts and Formulae, second ed., Birkhäuser, Basel, 2002. | Zbl 1012.60003

[5] M. Dominé, First passage time distribution of a Wiener process with drift concerning two elastic barriers, J. Appl. Probab. 33 (1996) 164-175. | MR 1371964 | Zbl 0867.60023

[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 0959.60073

[7] J.M. Harrison, Brownian Motion and Stochastic Flow Systems, Wiley, New York, 1985. | MR 798279 | Zbl 0659.60112

[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. | MR 2036278 | Zbl 1051.60083

[9] H.P. Mckean, Stochastic Integrals, Academic Press, New York, 1969. | MR 247684 | Zbl 0191.46603

[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. | MR 620995 | Zbl 0469.60076

[11] J. Pitman, M. Yor, A decomposition of Bessel bridges, Z. Wahrsch. Verw. Gebiete 59 (1982) 425-457. | MR 656509 | Zbl 0484.60062

[12] J. Pitman, M. Winkel, Growth of the Brownian forest, Ann. Probab. 33 (6) (2005) 2188-2211. | MR 2184095 | Zbl 1092.60033

[13] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, third ed., Springer-Verlag, Berlin, 2001. | Zbl 0804.60001

[14] E. Tanré, P. Vallois, Range of Brownian motion with drift, J. Theor. Probab. 19 (1) (2006) 45-69. | MR 2256479 | Zbl 1101.60063