Concerning the Moment Convergence Result for Properly Normalised Delayed Sums |Chapter 2| Research Updates in Mathematics and Computer Science Vol. 8

 

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 𝑇𝑛=𝑆𝑛+𝑎𝑛−𝑆𝑛=𝑛+𝑎𝑛∑𝑘=𝑛+1𝑋𝑘. 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.

 

Author(s) Details

Kokkada Vidyalaxmi

Department of Studies in Statistics, Manasagangotri, University of Mysore, Mysuru – 570 006, Karnataka, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/rumcs/v8/304