On convergence of the distributions of random sequences with independent random indexes to variance-mean mixtures

2014/10/04 by V. Yu. Korolev, Korolev, V. Yu., Alexander Zeifman +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1410.1022

openalex publication_date 2014/10/04 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient conditions for the convergence of randomly indexed random sequences. Special attention is paid to the case where the elements of the basic double array are formed as cumulative sums of independent not necessarily identically distributed random variables. Using simple moment-type conditions we prove the theorem on convergence of the distributions of such sums to normal variance-mean mixtures.

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