On maximum increase and decrease of brownian motion

Paavo Salminen; Pierre Vallois

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 6, page 655-676
  • ISSN: 0246-0203

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Salminen, Paavo, and Vallois, Pierre. "On maximum increase and decrease of brownian motion." Annales de l'I.H.P. Probabilités et statistiques 43.6 (2007): 655-676. <http://eudml.org/doc/77950>.

@article{Salminen2007,
author = {Salminen, Paavo, Vallois, Pierre},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {-transform; time reversal; path decompositions; Brownian motion with drift; excursion process; maximum process; Itô measure; maximum drawdown; covariance; catalan's constant},
language = {eng},
number = {6},
pages = {655-676},
publisher = {Elsevier},
title = {On maximum increase and decrease of brownian motion},
url = {http://eudml.org/doc/77950},
volume = {43},
year = {2007},
}

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
PB - Elsevier
VL - 43
IS - 6
SP - 655
EP - 676
LA - eng
KW - -transform; time reversal; path decompositions; Brownian motion with drift; excursion process; maximum process; Itô measure; maximum drawdown; covariance; catalan's constant
UR - http://eudml.org/doc/77950
ER -

References

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  9. [9] H.P. McKean, Stochastic Integrals, Academic Press, New York, 1969. Zbl0191.46603MR247684
  10. [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. Zbl0469.60076MR620995
  11. [11] J. Pitman, M. Yor, A decomposition of Bessel bridges, Z. Wahrsch. Verw. Gebiete59 (1982) 425-457. Zbl0484.60062MR656509
  12. [12] J. Pitman, M. Winkel, Growth of the Brownian forest, Ann. Probab.33 (6) (2005) 2188-2211. Zbl1092.60033MR2184095
  13. [13] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, third ed., Springer-Verlag, Berlin, 2001. Zbl0804.60001
  14. [14] E. Tanré, P. Vallois, Range of Brownian motion with drift, J. Theor. Probab.19 (1) (2006) 45-69. Zbl1101.60063MR2256479

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