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High-frequency asymptotics for subordinated stationary fields on an Abelian compact group

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  • Marinucci, Domenico
  • Peccati, Giovanni

Abstract

Let be a random field indexed by an Abelian compact group G, and suppose that has the form , where T is Gaussian and stationary. The aim of this paper is to establish high-frequency central limit theorems for the Fourier coefficients associated with . The proofs of our main results involve recently established criteria for the weak convergence of multiple Wiener-Itô integrals. Our research is motivated by physical applications, mainly related to the probabilistic modelling of the cosmic microwave background radiation. In this connection, the case of the n-dimensional torus is analyzed in detail.

Suggested Citation

  • Marinucci, Domenico & Peccati, Giovanni, 2008. "High-frequency asymptotics for subordinated stationary fields on an Abelian compact group," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 585-613, April.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:4:p:585-613
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    References listed on IDEAS

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    1. Baldi, Paolo & Marinucci, Domenico, 2007. "Some characterizations of the spherical harmonics coefficients for isotropic random fields," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 490-496, March.
    2. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
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    1. Marinucci, D. & Peccati, G., 2010. "Representations of SO(3) and angular polyspectra," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 77-100, January.
    2. Chen, Huiping & Chen, Yong & Liu, Yong, 2024. "Kernel representation formula: From complex to real Wiener–Itô integrals and vice versa," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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