A Central Limit Theorem for Periodograms Under Rho-Prime Mixing
Robert J. Niichel
TL;DR
This paper proves a multivariate Central Limit Theorem for sums of dependent complex-valued random variables with rho-prime mixing, extending CLT applicability to dependent data indexed by multi-dimensional integer grids.
Contribution
It introduces a CLT for rectangular sums of rho-prime-mixing variables, broadening theoretical understanding of dependent data in multiple dimensions.
Findings
Establishes a multivariate CLT for rho-prime-mixing variables
Extends CLT results to complex-valued, dependent data in Z^d
Provides a theoretical foundation for spectral analysis of dependent processes
Abstract
This paper consists of a proof of a multivariate Central Limit Theorem for "rectangular" sums of dependent complex-valued, rho-prime-mixing random variables indexed by Z^d.
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Taxonomy
Topicsadvanced mathematical theories · Mathematical Dynamics and Fractals · Stochastic processes and statistical mechanics