On the equivalence of limit distributions of a sum and of a maximum sum of independent random variables

DOI10.1016/j.spl.2010.01.020zbMath1198.60017OpenAlexW2072179145MaRDI QIDQ968474

Sreehari Maddipatla

Publication date: 5 May 2010

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2010.01.020

zbMATH Keywords

domain of attractionstable distributionmoment inequalitylimit distribution of maximum sumsupremum of a stable process

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

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Extreme value distributions for two kinds of path sums of Markov chain

Cites Work

• The law of the supremum of a stable Lévy process with no negative jumps
• Weak convergence of superpositions of randomly selected partial sums
• Limit Theorems for the Maximal Random Sums
• A limit theorem for random walks with drift
• On a Class of Limit Distributions for Normalized Sums of Independent Random Variables
• Maxima of sums of random variables and suprema of stable processes
• On certain limit theorems of the theory of probability