Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the Law of Large Numbers and Convergence Rates for the Discrete Fourier Transform of Random Fields

Vishakha

Abstract

We study the Marcinkiewicz-Zygmund strong law of large numbers for the cubic partial sums of the discrete Fourier transform of random fields. We establish Marcinkiewicz-Zygmund types rate of convergence for the discrete Fourier transform of random fields under weaker conditions than identical distribution.

On the Law of Large Numbers and Convergence Rates for the Discrete Fourier Transform of Random Fields

Abstract

We study the Marcinkiewicz-Zygmund strong law of large numbers for the cubic partial sums of the discrete Fourier transform of random fields. We establish Marcinkiewicz-Zygmund types rate of convergence for the discrete Fourier transform of random fields under weaker conditions than identical distribution.
Paper Structure (12 sections, 9 theorems, 78 equations)

This paper contains 12 sections, 9 theorems, 78 equations.

Table of Contents

  1. Introduction
  2. Notations
  3. Main results
  4. Lemmas
  5. Proof of main results
  6. Proof of Theorem \ref{['Theorem1']}
  7. Proof of Theorem \ref{['Theorem2']}
  8. Proof of Theorem \ref{['Theorem3']}
  9. Proof of Theorem \ref{['Theorem4']}
  10. Proof of Theorem \ref{['Theorem5']}
  11. Proof of Remark \ref{['remark1']}
  12. Appendix

Key Result

Theorem 3.1

Assume $(X_{\textbf{n}})_{\textbf{n}}$ satisfies condition If $E|X| < \infty$, then

Theorems & Definitions (22)

  • Theorem 3.1
  • Theorem 3.2
  • Theorem 3.3
  • Theorem 3.4
  • Remark 3.1
  • Theorem 3.5
  • Remark 3.2
  • Remark 3.3
  • Lemma 4.1
  • proof
  • ...and 12 more