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April, 1987 Markov Additive Processes II. Large Deviations
P. Ney, E. Nummelin
Ann. Probab. 15(2): 593-609 (April, 1987). DOI: 10.1214/aop/1176992160

Abstract

Let $\{(X_n, S_n); n = 0,1,\ldots\}$ be a Markov additive process, $\{X_n\}$ taking values in a general state space $\mathbb{E}$, while $\{S_n\} \subset \mathbb{R}^d$. The large deviation principle is shown to hold for $P_x\{(X_n, S_n) \in A \times n\Gamma\}, A \subset \mathbb{E}, \Gamma \subset \mathbb{R}^d$, the upper bound holding for closed sets $\Gamma$, the lower bound for open sets. The only hypothesis for the lower bound is irreducibility of $\{X_n\}$, and nonsingularity of $\{S_n\}$. The rate function is characterized in terms of the transform kernel of $P_x$.

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P. Ney. E. Nummelin. "Markov Additive Processes II. Large Deviations." Ann. Probab. 15 (2) 593 - 609, April, 1987. https://doi.org/10.1214/aop/1176992160

Information

Published: April, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0625.60028
MathSciNet: MR885132
Digital Object Identifier: 10.1214/aop/1176992160

Subjects:
Primary: 60F10
Secondary: 60J05 , 60K15

Keywords: large deviations , Markov additive process , Markov chain

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 2 • April, 1987
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