Concerning the Moment Convergence Result for Properly Normalised Delayed Sums - Kokkada Vidyalaxmi (Research Updates in Mathematics and Computer Science Vol. 8, 2024)
Let Xn, n\(\)1 be a sequence of independent and identically distributed random variables with a common distribution function F. Let (Sn) be the partial sum sequence. Set T_n=S_n+a_n-S_n=_k=n+1^n+a_n X_k. The sum Tn is referred to as a (forward) delayed sum. We derive a moment convergence result for the delayed sums when the random variables are within the domain of normal attraction of a stable law with an index \(α\), 1 < \(α\) < 2 The results can be used to obtain a density version of a local limit theorem.