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Research Article Open access CC BY 4.0

On Moment Convergence Result for Properly Normalized Delayed Sums

Kokkada Vidyalaxmi, Gooty Divanji

Journal of Advances in Mathematics and Computer Science · pp. 36–43 · Published 21 Jul 2022

10.9734/jamcs/2022/v37i630459

Abstract

Let  \(\left\{X_{n}, n \geq 1\right\}\)  be a sequence of independent and identically distributed random  variables with a common distribution function F. Let  \((S_{n})\) be the partial sum sequence. Set  \(T_{n}=S_{n+a_{n}}-S_{n}=\sum_{k=n+1}^{n+a_{n}} X_{k}\) The sum  (T_{n}\) is called a (forward) delayed sum. The present work aims to obtain a moment convergence result for the delayed sums when the random variables are in the domain of normal attraction of a stable law with an index  \(\alpha ,1, < \alpha < 2 \).  This result plays a vital role in studying a local limit theorem.

Domain of normal attraction stable law delayed sum moment convergence local limit theorem

References (4)

  1. 1 An Introduction to Probability Theory and Its Applications. [DOI]
  2. 2 Limit Distributions for Sums of Independent Random Variables. [DOI]
  3. 3 PROBABILITY AND POTENTIALS [DOI]
  4. 4 Limit Theorems for Delayed Sums [DOI]

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