Sharp asymptotics of large deviations for general state-space Markov-additive chains in \(\mathbb{R}^d\)
type: Item
instance of: scholarly article
title: Sharp asymptotics of large deviations for general state-space Markov-additive chains in \(\mathbb{R}^d\)
zbMATH Open document ID: 0988.60012
DOI: 10.1016/S0167-7152(99)00181-9
author: Michael Iltis
published in: Statistics \& Probability Letters
publication date: 2002-07-10T00:00:00Z
review text: Let \(X_N\) be a Markov chain with state-space \(E\), \(\sigma\)-field \(\mathcal E\), assumed to be irreducible with respect to a maximal irreducibility measure \(\varphi\) on \((E,{\mathcal E})\) and aperiodic. Consider a time-homogeneous Markov-additive chain \((X_N,S_N)\), \(N=0,1,2,\dots\), where \(S_N=\sum^N_{i=0}\xi_i\) while \((X_N,\xi_N)\) is a Markov chain taking values in the space \(E\times\mathbb{R}^d\). Using tilted split-chain distribution, a representation formula for large deviations has been reported. Asymptotic results of the form \[ P(S_N\in N\Gamma; x_N\in A)=N^r e^{-Na}(d_0+o(1)) \] as \(N\to \infty\) are obtained.
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 1448744
zbMATH Keywords: large deviations
zbMATH Keywords: rate function
zbMATH Keywords: Markov-additive random variables
zbMATH Keywords: regenerative process
reviewed by: V. Thangaraj
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1448744