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

Domenico Marinucci and Giovanni Peccati

Stochastic Processes and their Applications, 2008, vol. 118, issue 4, 585-613

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.

Keywords: Gaussian; fields; Stationary; fields; Isotropic; fields; Central; limit; theorems; Abelian; groups; Multiple; Wiener-Ito; integrals (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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