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April, 1987 Markov Additive Processes I. Eigenvalue Properties and Limit Theorems
P. Ney, E. Nummelin
Ann. Probab. 15(2): 561-592 (April, 1987). DOI: 10.1214/aop/1176992159


We consider a Markov additive process $\{(X_n, S_n): n = 0, 1,\ldots\}$, where $\{X_n\}$ is a M.C. on a general state space and $S_n$ is an $\mathbb{R}^d$-valued additive component. Limit theory for $S_n$ is studied via properties of the eigenvalues and eigenfunctions of the kernel of generating functions associated with the transition function of the process. The emphasis is on large deviation theory, but some other limit theorems are also given.


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P. Ney. E. Nummelin. "Markov Additive Processes I. Eigenvalue Properties and Limit Theorems." Ann. Probab. 15 (2) 561 - 592, April, 1987.


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

zbMATH: 0625.60027
MathSciNet: MR885131
Digital Object Identifier: 10.1214/aop/1176992159

Primary: 60F10
Secondary: 60J05 , 60K15

Keywords: large deviations , Markov additive process , Markov chain

Rights: Copyright © 1987 Institute of Mathematical Statistics

Vol.15 • No. 2 • April, 1987
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