Limit distributions of sums of random variables defined on a finite homogeneous Markov chain. II
type: Item
instance of: scholarly article
title: Limit distributions of sums of random variables defined on a finite homogeneous Markov chain. II
zbMATH Open document ID: 0833.60068
DOI: 10.1007/BF02335394
author: Yanyan Li
published in: Lithuanian Mathematical Journal
publication date: 1995-09-18T00:00:00Z
review text: [For part I see above.] Here the author considers the random variable \(S_{n,N} = \sum^n_{j = 1} a_N (X_{N_j})\), where now \(a_N(i)\), \(N \geq 1\), denotes the \(i\)-th coordinate of the sequence of vectors \(a_N \in R^n\), and \(X_N = (X_{N_j}\), \(j \geq 0)\), \(N \geq 1\), is the series of homogeneous Markov chains with a finite space \([d] = \{1, 2, \dots, d\}\) and irreducible transition matrix. All possible limit distributions of the appropriately centralized and normalized sums \(S_{n,N}\) are described.
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 794515
zbMATH Keywords: sums of random variables
zbMATH Keywords: Markov chain
zbMATH Keywords: weak convergence
zbMATH Keywords: irreducible transition matrix
reviewed by: N. S. Bratijchuk
MaRDI profile type: Publication
cites work: Limit distributions of sums of random variables defined on a finite homogeneous Markov chain. I
full work available at URL: https://doi.org/10.1007/bf02335394
OpenAlex ID: W1972037331
description: scientific article; zbMATH DE number 794515