Geodesic
Conditioning of gaussian functionals
Teoriâ slučajnyh processov, Tome 13 (2007) no. 3, pp. 29-37.

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In the article, we consider terms of the Gaussian chaotic expansion under conditioning with respect to some sigma-field and discuss the possibility to organize the orthogonal expansion from them.
Keywords: Gaussian white noise, Ito–Wiener expansion, conditional expectation, polynomially nondegenerate measure. 
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Andrey A. Dorogovtsev. Conditioning of gaussian functionals. Teoriâ slučajnyh processov, Tome 13 (2007) no. 3, pp. 29-37. http://geodesic.mathdoc.fr/item/THSP_2007_13_3_a3/

[1] D. Nualart, The Malliavin Calculus and Related Topics, Springer, New York, 1995

[2] M. Sanz–Solé, Malliavin Calculus. With Applications to Stochastic Partial Differential Equations, EPEL Press, Lausanne, 2005

[3] A. A. Dorogovtsev, Stochastic Analysis and Random Maps in Hilbert Space, VSP, Utrecht, Tokyo, 1994

[4] T. Sekiguchi, Y. Shyota, “$L_2$-theory of non-causal stochastic integrals”, Math. Reports Toyama Univ., 85:8 (1985), 119-–195

[5] A. A. Dorogovtsev, “Stochastic integral with respect to Arratia flow”, Dokl. Akad. Nauk, 410:2 (2006), 156-–157

[6] N. I. Portenko, “On multidimensional skew Brownian motion and the Feynman–Kac formula”, Stochastic Processes, 4:1–2 (1998), 60-–70

[7] Le J. Yves, R. Olivier, “Flows, coalescense and noise”, Ann. Probab., 32:2 (2004), 1247-–1315

[8] A. A. Dorogovtsev, “Measurable functionals and ?nitely absolutely continuous measures on Banach space”, Ukrainian. Math. Journ., 52:9 (2000), 1194-–1204

[9] V. E. Berezhnoy, “On the equivalence of norms on the space of $\gamma$-measurable polynomials”, Moscow Univ. Bull., Ser. Math., 2004, no. 4, 54-–56