The Annals of Probability

Markov Additive Processes I. Eigenvalue Properties and Limit Theorems

P. Ney and E. Nummelin

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Abstract

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.

Article information

Source
Ann. Probab., Volume 15, Number 2 (1987), 561-592.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992159

Digital Object Identifier
doi:10.1214/aop/1176992159

Mathematical Reviews number (MathSciNet)
MR885131

Zentralblatt MATH identifier
0625.60027

JSTOR
links.jstor.org

Subjects
Primary: 60F10: Large deviations
Secondary: 60K15: Markov renewal processes, semi-Markov processes 60J05: Discrete-time Markov processes on general state spaces

Keywords
Large deviations Markov chain Markov additive process

Citation

Ney, P.; Nummelin, E. Markov Additive Processes I. Eigenvalue Properties and Limit Theorems. Ann. Probab. 15 (1987), no. 2, 561--592. doi:10.1214/aop/1176992159. https://projecteuclid.org/euclid.aop/1176992159


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See also

  • Part II: P. Ney, E. Nummelin. Markov Additive Processes II. Large Deviations. Ann. Probab., Volume 15, Number 2 (1987), 593--609.