On the Law of Large Numbers for Discrete Fourier Transform
Na Zhang
TL;DR
This paper investigates the convergence rate of the discrete Fourier transform of i.i.d. random variables with finite p-th moments, extending the understanding of the strong law of large numbers in this context.
Contribution
It establishes the convergence rate of the discrete Fourier transform under finite p-th moments for 1<p<2, which was previously not well understood.
Findings
Convergence rate of discrete Fourier transform established
Results applicable for variables with finite moments of order p
Extends classical strong law of large numbers to Fourier transforms
Abstract
We establish the rate of convergence in the strong law of large numbers of discrete Fourier Transform of the identically distributed random variables with finite moment of order p, where 1<p<2.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Mathematical Approximation and Integration