Transformations of Two Independent Brownian Motions and Orthogonal Decompositions of Brownian Filtrations
Y. Ouknine, M. Erraoui

1.	Alili L., Wu C. T., Further results on some singular linear stochastic differential equations, arXiv: math/0702785
2.	Brockhaus O., “Sufficient statistics for the Brownian sheet”, Lecture Notes in Math., 1557, 1991, 44–52
3.	Cairoli R., Walsh J. B., “Stochastic integrals in the plane”, Acta Math., 134 (1975), 111–183
4.	Chaleyat-Maurel M., Jeulin T., “Grossissement gaussien de la filtration brownienne”, Lecture Notes in Math., 1118, 1985, 59–109
5.	Cramér H., “On some classes of nonstationary processes”, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, v. II, Univ. of California Press, Berkeley, 57–78
6.	Deheuvels P., “Invariance of Wiener processes and of Brownian bridges by integral transforms and applications”, Stochastic Process. Appl., 13:3 (1982), 311–318
7.	Decreusefond L., Üstünel A. S., “Stochastic analysis of the fractional Brownian motion”, Potential Anal., 10:2 (1998), 177–214
8.	Föllmer H., Wu C.-T., Yor M., “Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading”, Stochastic Process. Appl., 84:1 (1999), 137–164
9.	Jeulin T., Semi-martingales et grossissement d'une filtration, Lecture Notes in Math., 833, 1980, 142 pp.
10.	Jeulin T., Yor M., “Une décomposition non-canonique du drap brownien”, Lecture Notes in Math., 1526, 1992, 322–347
11.	Jeulin T., Yor M., “Filtrations des ponts browniens et équations différentielles stochastiques linéaires”, Lecture Notes in Math., 1426, 1990, 227–265
12.	Hibino Y., “Another noncanonical representation of a Brownian motion related to singular Volterra kernels”, Proceedings of the Meijo Winter School 2003 “Quantum Information and Complexity”, eds. T. Hida, K. Saito, and Si Si, World Scientific, Singapore, 2004, 202–210
13.	Hibino Y., Hitsuda M., “Canonical property of representations of Gaussian processes with singular Volterra kernels”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 5:2 (2002), 293–296
14.	Hibino Y., Hitsuda M., Muraoka H., “Construction of noncanonical representations of a Brownian motion”, Hiroshima Math. J., 27:3 (1997), 439–448
15.	Hibino Y., “Noncanonical representations of a multi-dimensional Brownian motion”, Quantum Information and Computing, Quantum Probability and White Noise Analysis, 19, eds. L. Accardi, M. Ohya, N. Watanabe, World Scientific, Singapore, 2006, 181–185
16.	Hida T., “Canonical representation of Gaussian processes and their applications”, Mem. Coll. Sci. Univ. Kyoto, 33 (1960), 109–155
17.	Lévy P., “Fonctions aléatoires à corrélation linéaire”, Illinois J. Math., 1 (1957), 217–258
18.	Meyer P.-A., “Sur une transformation du mouvement brownien due à Jeulin et Yor”, Lecture Notes in Math., 1583, 1994, 98–101
19.	Wu C.-T., Yor M., “Linear transformation of two independent Brownian motions and orthogonal decompositions of Brownian filtrations”, Publ. Mat., 46:1 (2002), 237–256
20.	Yor M., Some Aspects of Brownian Motion. Part I. Some Special Functionals, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, 1992, 136 pp.
21.	Yor M., Some Aspects of Brownian Motion. Part II. Some Recent Martingale Problems, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, 1997, 144 pp.