Fubini's theorem for double Wiener integrals and the variance of the brownian path
Annales de l'I.H.P. Probabilités et statistiques, Volume 27 (1991) no. 2, p. 181-200
@article{AIHPB_1991__27_2_181_0,
     author = {Donati-Martin, Catherine and Yor, Marc},
     title = {Fubini's theorem for double Wiener integrals and the variance of the brownian path},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {27},
     number = {2},
     year = {1991},
     pages = {181-200},
     zbl = {0738.60074},
     mrnumber = {1118933},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1991__27_2_181_0}
}
Donati-Martin, C.; Yor, M. Fubini's theorem for double Wiener integrals and the variance of the brownian path. Annales de l'I.H.P. Probabilités et statistiques, Volume 27 (1991) no. 2, pp. 181-200. http://www.numdam.org/item/AIHPB_1991__27_2_181_0/

[1] (a) Ph. Biane and M. Yor, A Relation Between Lévy's Stochastic Area Formula, Legendre Polynomials and Some Continued Fractions of Gauss, Tech. Report n° 74, Dpt. of Statistics, University of California, Berkeley (1986). (b) Ph Biane and M. Yor, Variations sur une formule de Paul Lévy. Ann. Inst. H. Poincaré, Vol. 23, 1987, pp. 359-377. | Numdam | Zbl 0623.60099

[2] T.S. Chiang, Y. Chow and Y.J. Lee, A formula for Ew[exp-2-1a2∥x+y∥22], Proceedings of the A.M.S., Vol. 100, No. 4, August 1987, pp. 721-724. | MR 894444 | Zbl 0641.60006

[3] B. Duplantier, Areas of Planar Brownian Curves. J. Phys. A. Math. Gen., Vol. 22, 1989, pp. 3033-3048. | MR 1007231 | Zbl 0717.60094

[4] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland-Kodansha, 1981; second edition, 1989. | MR 1011252 | Zbl 0495.60005

[5] T. Chan, K. Jansons and L.C.G. Rogers, Polymers in Elongational Flows, in preparation, December 1989.

[6] P. Krée, A Remark on Paul Lévy's Stochastic Area Formula, Aspect of Mathematics and its Applications, J. BARROSO éd., Elsevier Science Publishers, B.V., 1986. | Zbl 0591.60013

[7] P. Lévy, Wiener's Random Function, and other Laplacian Random Functions, Proc. 2nd Berkeley Symp. Math. Stat. Prob., Vol. II, 1950, pp. 171-186, University of California. | MR 44774 | Zbl 0044.13802

[8] P. Malliavin, Ck Hypoellipticity with Degeneracy, Part II, Stochastic Analysis, A. FRIEDMAN and M. PINSKY Eds, Academic Press, 1978, pp. 327-341. | MR 517250 | Zbl 0449.58023

[9] P. Mcaonghusa and J.V. Pulé, An Extension of Lévy's Stochastic Area Formula, Stochastics and Stochastics Reports, Vol. 26, 1989, pp. 247-255. | MR 1056073 | Zbl 0676.60072

[10] J. Pitman and M. Yor, A Decomposition of Bessel Bridges. Z. Wahr, Vol. 59, 1982, pp. 425-457. | MR 656509 | Zbl 0484.60062

[11] D. Williams, On a Stopped Brownian Motion Formula of H. M. Taylor. Sém. Probas X, Lect. Notes Maths, Vol. 511, 1976, pp. 235-239. | Numdam | MR 461687 | Zbl 0368.60056

[12] M. Yor, Remarques sur une formule de Paul Lévy, Séminaire de Probabilités XIV, Lect. Notes Maths, No. 850, Springer, 1980, pp. 343-346. | Numdam | MR 580140 | Zbl 0429.60045

[13] M. Yor, On Stochastic Areas and Averages of Planar Brownian Motion. J. Phys. A. Math. Gen., Vol. 22, 1989, pp. 3049-3057. | MR 1007232 | Zbl 0717.60095

[14] T. Chan, Indefinite Quadratic Functionals of Gaussian Processes and Least-Action Paths, Ann. Inst. H. Poincaré, Vol. 27, n° 2, 1991, pp. 239-271. | Numdam | MR 1118937 | Zbl 0745.60034

[15] J.J. Prat, Equation de Schrödinger: Analyticité transverse de la densité de la loi d'une fonctionnelle additive, Bull. Sci. Maths, Vol. 115, n° 2, 1991, pp. 133-176. | MR 1101021 | Zbl 0745.60057