## The Annals of Probability

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

### Markov Additive Processes I. Eigenvalue Properties and Limit Theorems

P. Ney and E. Nummelin

#### 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

#### See also

- Part II: P. Ney, E. Nummelin. Markov Additive Processes II. Large Deviations. Ann. Probab., Volume 15, Number 2 (1987), 593--609.Project Euclid: euclid.aop/1176992160