Transformations of Two Independent Brownian Motions and Orthogonal Decompositions of Brownian Filtrations
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 769-786
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we consider certain classes of transformations of two independent Brownian motions. We will give a new orthogonal decomposition of some Brownian filtrations.
Keywords: Brownian motion, Brownian filtration, canonical decomposition, Hardy operators.
@article{TVP_2008_53_4_a6,
     author = {Y. Ouknine and M. Erraoui},
     title = {Transformations of {Two} {Independent} {Brownian} {Motions} and {Orthogonal} {Decompositions} of {Brownian} {Filtrations}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {769--786},
     year = {2008},
     volume = {53},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a6/}
}
TY  - JOUR
AU  - Y. Ouknine
AU  - M. Erraoui
TI  - Transformations of Two Independent Brownian Motions and Orthogonal Decompositions of Brownian Filtrations
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2008
SP  - 769
EP  - 786
VL  - 53
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a6/
LA  - en
ID  - TVP_2008_53_4_a6
ER  - 
%0 Journal Article
%A Y. Ouknine
%A M. Erraoui
%T Transformations of Two Independent Brownian Motions and Orthogonal Decompositions of Brownian Filtrations
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2008
%P 769-786
%V 53
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a6/
%G en
%F TVP_2008_53_4_a6
Y. Ouknine; M. Erraoui. Transformations of Two Independent Brownian Motions and Orthogonal Decompositions of Brownian Filtrations. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 769-786. http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a6/

[1] Alili L., Wu C. T., Further results on some singular linear stochastic differential equations, arXiv: math/0702785 | MR

[2] Brockhaus O., “Sufficient statistics for the Brownian sheet”, Lecture Notes in Math., 1557, 1991, 44–52 | MR

[3] Cairoli R., Walsh J. B., “Stochastic integrals in the plane”, Acta Math., 134 (1975), 111–183 | DOI | MR | Zbl

[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 | MR

[6] Deheuvels P., “Invariance of Wiener processes and of Brownian bridges by integral transforms and applications”, Stochastic Process. Appl., 13:3 (1982), 311–318 | DOI | MR | Zbl

[7] Decreusefond L., Üstünel A. S., “Stochastic analysis of the fractional Brownian motion”, Potential Anal., 10:2 (1998), 177–214 | DOI | MR

[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 | DOI | MR | Zbl

[9] Jeulin T., Semi-martingales et grossissement d'une filtration, Lecture Notes in Math., 833, 1980, 142 pp. | MR | Zbl

[10] Jeulin T., Yor M., “Une décomposition non-canonique du drap brownien”, Lecture Notes in Math., 1526, 1992, 322–347 | MR | Zbl

[11] Jeulin T., Yor M., “Filtrations des ponts browniens et équations différentielles stochastiques linéaires”, Lecture Notes in Math., 1426, 1990, 227–265 | MR | Zbl

[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 | DOI | MR | Zbl

[14] Hibino Y., Hitsuda M., Muraoka H., “Construction of noncanonical representations of a Brownian motion”, Hiroshima Math. J., 27:3 (1997), 439–448 | MR | Zbl

[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 | Zbl

[16] Hida T., “Canonical representation of Gaussian processes and their applications”, Mem. Coll. Sci. Univ. Kyoto, 33 (1960), 109–155 | MR | Zbl

[17] Lévy P., “Fonctions aléatoires à corrélation linéaire”, Illinois J. Math., 1 (1957), 217–258 | MR | Zbl

[18] Meyer P.-A., “Sur une transformation du mouvement brownien due à Jeulin et Yor”, Lecture Notes in Math., 1583, 1994, 98–101 | MR | Zbl

[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 | MR | Zbl

[20] Yor M., Some Aspects of Brownian Motion. Part I. Some Special Functionals, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, 1992, 136 pp. | MR

[21] Yor M., Some Aspects of Brownian Motion. Part II. Some Recent Martingale Problems, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, 1997, 144 pp. | MR | Zbl