On weak brownian motions of arbitrary order
Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 4, pp. 447-487. 
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     author = {F\"ollmer, Hans and Wu, Ching-Tang and Yor, Marc},
     title = {On weak brownian motions of arbitrary order},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {447--487},
     publisher = {Gauthier-Villars},
     volume = {36},
     number = {4},
     year = {2000},
     mrnumber = {1785391},
     zbl = {0968.60069},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2000__36_4_447_0/}
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Föllmer, Hans; Wu, Ching-Tang; Yor, Marc. On weak brownian motions of arbitrary order. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 4, pp. 447-487. http://www.numdam.org/item/AIHPB_2000__36_4_447_0/

[1] Carmona Ph., Petit F., Yor M., A trivariate law for certain processes related to perturbed Brownian motions, 1999, submitted.

[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. | Numdam | MR | Zbl

[3] Deheuvels P., Invariance of Wiener processes and of Brownian bridges by integral transformations and applications, Stochastic Processes and Their Applications 13 (1982) 311-318. | MR | Zbl

[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. | MR | Zbl

[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. | Numdam | MR | Zbl

[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 Applications 84 (1) (1999) 137-164. | MR | Zbl

[7] Gyöngy I., Mimicking the one-dimensional marginal distributions of processes having an Itô differential, Probab. Theory Related Fields 71 (1986) 501-516. | MR | Zbl

[8] Hibino Y., Hitsuda M., Muraoka H., Construction of noncanonical representations of a Brownian motion, Math. J. 27 (1997) 439-448. | MR | Zbl

[9] Hida T., Hitsuda M., Gaussian Processes, American Mathematical Society, 1993. | MR | Zbl

[10] Hitsuda M., Representation of Gaussian processes equivalent to Wiener process, Osaka J. Math. 5 (1968) 299-312. | MR | Zbl

[11] Kazamaki N., Changes of times, stochastic integrals and weak martingales, Z. Wahrscheinlichkeitstheor. Verw. Geb. 22 (1972) 25-32. | MR | Zbl

[12] Kazamaki N., On a stochastic integral equation with respect to a weak martingale, Tohoku Math. J. 26 (1974) 53-63. | MR | Zbl

[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. | Numdam | MR | Zbl

[14] Lévy P., Fonctions aléatoires à corrélations linéaires, Illinois J. Math. 1 (1957) 217- 258. | MR | Zbl

[15] Neveu J., Processus Aléatoires Gaussiens, Les Presses de l'Université de Montréal, 1968. | MR | Zbl

[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] Pitman J., Yor M., Quelques identités en loi pour les processus de Bessel, Astérisque 236 (1996) 249-276. Hommage à P. A. Meyer et J. Neveu. | Numdam | MR | Zbl

[18] Rényi A., Remarks on the Poisson process, Studia Sci. Math. Hung. 2 (1967) 119- 123. | MR | Zbl

[19] Revuz D., Yor M., Continuous Martingales and Brownian Motion, Springer, 1991. | MR | Zbl

[20] Stoyanov J., Counterexamples in Probability, 1st ed., Wiley, 1987. | MR | Zbl

[21] Stoyanov J., Counterexamples in Probability, 2nd ed., Wiley, 1997. | MR | Zbl

[22] Szász D.O.H., Once more on the Poisson process, Studia Sci. Math. Hung. 5 (1970) 441-444. | MR | Zbl

[23] Yor M., Some Aspects of Brownian Motion, Part II: Some Recent Martingale Problems, Birkhäuser, Basel, 1997. | MR | Zbl