On weak brownian motions of arbitrary order

Hans Föllmer; Ching-Tang Wu; Marc Yor

Annales de l'I.H.P. Probabilités et statistiques (2000)

  • Volume: 36, Issue: 4, page 447-487
  • ISSN: 0246-0203

How to cite

top

Föllmer, Hans, Wu, Ching-Tang, and Yor, Marc. "On weak brownian motions of arbitrary order." Annales de l'I.H.P. Probabilités et statistiques 36.4 (2000): 447-487. <http://eudml.org/doc/77668>.

@article{Föllmer2000,
author = {Föllmer, Hans, Wu, Ching-Tang, Yor, Marc},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {weak Brownian motion; marginal distributions; Wiener measure; Brownian motion; Volterra kernel},
language = {eng},
number = {4},
pages = {447-487},
publisher = {Gauthier-Villars},
title = {On weak brownian motions of arbitrary order},
url = {http://eudml.org/doc/77668},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Föllmer, Hans
AU - Wu, Ching-Tang
AU - Yor, Marc
TI - On weak brownian motions of arbitrary order
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2000
PB - Gauthier-Villars
VL - 36
IS - 4
SP - 447
EP - 487
LA - eng
KW - weak Brownian motion; marginal distributions; Wiener measure; Brownian motion; Volterra kernel
UR - http://eudml.org/doc/77668
ER -

References

top
  1. [1] Carmona Ph., Petit F., Yor M., A trivariate law for certain processes related to perturbed Brownian motions, 1999, submitted. Zbl1060.60082
  2. [2] Chiu Y., From an example of Lévy's, in: Azéma J., Meyer P.A., Yor M. (Eds.), Séminaire de Probabilités XXIX, Lecture Notes in Mathematics, Vol. 1613, Springer, 1995, pp. 162-165. Zbl0833.60082MR1459457
  3. [3] Deheuvels P., Invariance of Wiener processes and of Brownian bridges by integral transformations and applications, Stochastic Processes and Their Applications13 (1982) 311-318. Zbl0491.60037MR671040
  4. [4] Dupire B., Pricing and hedging with smiles, in: Dempster M.A.H., Pliska S.R. (Eds.), Mathematics of Derivative Securities, Publications of the Newton Institute, Cambridge, 1997, pp. 103-111. Zbl0913.90012MR1491370
  5. [5] Föllmer H., Calcul d'Itô sans probabilités, in: Azéma J., Yor M. (Eds.), Séminaire de Probabilités XV, Lecture Notes in Mathematics, Vol. 850, Springer, 1981, pp. 143- 150. Zbl0461.60074MR622559
  6. [6] Föllmer H., Wu C.-T., Yor M., Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading, Stochastic Processes and Their Applications84 (1) (1999) 137-164. Zbl0996.60079MR1720102
  7. [7] Gyöngy I., Mimicking the one-dimensional marginal distributions of processes having an Itô differential, Probab. Theory Related Fields71 (1986) 501-516. Zbl0579.60043MR833267
  8. [8] Hibino Y., Hitsuda M., Muraoka H., Construction of noncanonical representations of a Brownian motion, Math. J.27 (1997) 439-448. Zbl0899.60035MR1482951
  9. [9] Hida T., Hitsuda M., Gaussian Processes, American Mathematical Society, 1993. Zbl0793.60002MR1216518
  10. [10] Hitsuda M., Representation of Gaussian processes equivalent to Wiener process, Osaka J. Math.5 (1968) 299-312. Zbl0174.49302MR243614
  11. [11] Kazamaki N., Changes of times, stochastic integrals and weak martingales, Z. Wahrscheinlichkeitstheor. Verw. Geb.22 (1972) 25-32. Zbl0213.19304MR310966
  12. [12] Kazamaki N., On a stochastic integral equation with respect to a weak martingale, Tohoku Math. J.26 (1974) 53-63. Zbl0302.60036MR358991
  13. [13] Lévy P., Sur une classe de courbes de l'espace de Hilbert et sur une équation intégrale non linéaire, Ann. Sci. Ecol. Norm. Sup. III. Ser.73 (1956) 121-156. Zbl0071.35003MR96303
  14. [14] Lévy P., Fonctions aléatoires à corrélations linéaires, Illinois J. Math.1 (1957) 217- 258. Zbl0077.12601MR100914
  15. [15] Neveu J., Processus Aléatoires Gaussiens, Les Presses de l'Université de Montréal, 1968. Zbl0192.54701MR272042
  16. [16] Petit F., Yor M., Itô's formula and the marginals of certain submartingales, in: Shiryaev A.N., Sulem A. (Eds.), Journées sur les Mathématiques Financières, Proceedings of INRIA (March 1999), 1998, pp. 164-167. 
  17. [17] Pitman J., Yor M., Quelques identités en loi pour les processus de Bessel, Astérisque236 (1996) 249-276. Hommage à P. A. Meyer et J. Neveu. Zbl0863.60035MR1417987
  18. [18] Rényi A., Remarks on the Poisson process, Studia Sci. Math. Hung.2 (1967) 119- 123. Zbl0149.12904MR212861
  19. [19] Revuz D., Yor M., Continuous Martingales and Brownian Motion, Springer, 1991. Zbl0731.60002MR1083357
  20. [20] Stoyanov J., Counterexamples in Probability, 1st ed., Wiley, 1987. Zbl0629.60001MR930671
  21. [21] Stoyanov J., Counterexamples in Probability, 2nd ed., Wiley, 1997. Zbl0884.60001MR930671
  22. [22] Szász D.O.H., Once more on the Poisson process, Studia Sci. Math. Hung.5 (1970) 441-444. Zbl0239.60047MR310981
  23. [23] Yor M., Some Aspects of Brownian Motion, Part II: Some Recent Martingale Problems, Birkhäuser, Basel, 1997. Zbl0880.60082MR1442263

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.