Decompositions of stochastic processes based on irreducible group representations
Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 2, pp. 304-336 Cet article a éte moissonné depuis la source Math-Net.Ru

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}
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G. Peccati; J.-R. Pycke. Decompositions of stochastic processes based on irreducible group representations. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 2, pp. 304-336. http://geodesic.mathdoc.fr/item/TVP_2009_54_2_a6/

[1] Adler R. J., An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, IMS Lecture Notes Monogr. Ser., 12, Inst. Math. Statist., Hayward, 1990, 160 pp. | MR | Zbl

[2] Chou C.-S., “Sur l'extension d'une identité en loi entre le pont brownien et la variance du mouvement brownien”, Stochastic Process. Appl., 49:2 (1994), 217–225 | DOI | MR | Zbl

[3] Deheuvels P., Peccati G., Yor M., “On quadratic functionals of the Brownian sheet and related processes”, Stochastic Process. Appl., 116:2 (2006), 493–538 | DOI | MR | Zbl

[4] Dellacherie C., Maisonneuve B., Meyer P.-A., Probabilités et Potentiel, Chapitres XVII à XXIV, Hermann, Paris, 1992

[5] Diaconis P., Group Representations in Probability and Statistics, IMS Lecture Notes Monogr. Ser., 11, Inst. Math. Statist., Hayward, 1988, 198 pp. | MR | Zbl

[6] Dudley R., Real Analysis and Probability, Cambridge Univ. Press, Cambridge, 2002, 555 pp. | MR

[7] Duistermaat J. J., Kolk J. A. C., Lie Groups, Springer-Verlag, Berlin, 1997, 344 pp. | MR

[8] Fox R., Taqqu M., “Multiple stochastic integrals with dependent integrators”, J. Multivariate Anal., 21:1 (1987), 105–127 | DOI | MR | Zbl

[9] James G. D., Liebeck M., Representations and Characters of Groups, Cambridge Univ. Press, New York, 2001, 458 pp. | MR

[10] Marinucci D., Peccati G., Group representations and high-resolution central limit theorems for subordinated spherical random fields, Preprint, 2008 | MR

[11] Marinucci D., Peccati G., “High-frequency asymptotics for subordinated stationary fields on an Abelian compact group”, Stochastic Process. Appl., 118:4 (2008), 585–613 | DOI | MR | Zbl

[12] Marinucci D., Peccati G., Representations of $SO(3)$ and angular polyspectra, Preprint, 2008 | MR

[13] Peccati G., Yor M., “Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections”, Approximation and Probability, Banach Center Publ., 72, Polish Acad. Sci., Warsaw, 2006, 235–250 | MR | Zbl

[14] Pycke J.-R., “Sur une identité en loi entre deux fonctionnelles quadratiques du pont Brownien”, C. R. Math. Acad. Sci. Paris, 340:5 (2005), 373–376 | MR | Zbl

[15] Pycke J.-R., “A decomposition for invariant tests of uniformity on the sphere”, Proc. Amer. Math. Soc., 135:9 (2007), 2983–2993 | DOI | MR | Zbl

[16] Rota G.-C., Shen J., “On the combinatorics of cumulants”, J. Combin. Theory Ser. A, 91:1–2 (2000), 283–304 | DOI | MR | Zbl

[17] Rota G.-C., Wallstrom T. C., “Stochastic integrals: a combinatorial approach”, Ann. Probab., 25:3 (1997), 1257–1283 | DOI | MR | Zbl

[18] Serfling R. J., Approximation Theorems of Mathematical Statistics, Wiley, New York, 1980, 371 pp. | MR | Zbl

[19] Serre J.-P., Linear Representations of Finite Groups, Grad. Texts in Math., 42, Springer-Verlag, New York–Heidelberg, 1977, 170 pp. | MR | Zbl

[20] Shi Z., Yor M., “On an identity in law for the variance of the Brownian bridge”, Bull. London Math. Soc., 29:1 (1997), 103–108 | DOI | MR | Zbl

[21] Shorack G. R., Wellner J. A., Empirical Processes with Applications to Statistics, Wiley, New York., 1986, 938 pp. | MR

[22] Slud E. V., “The moment problem for polynomial forms in normal random variables”, Ann. Probab., 21:4, 2200–2214 | DOI | MR | Zbl

[23] Surgailis D., “CLTs for polynomials of linear sequences: Diagram formula with illustrations”, Theory and Applications of Long-Range Dependence, eds. P. Doukhan et al., Birkhäuser, Boston, 2003, 111–127 | MR | Zbl

[24] Watson G. S., “Goodness-of-fit tests on a circle”, Biometrika, 48 (1961), 109–114 | MR | Zbl