Limit theorems for Markov chains of finite rank |
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Authors: | AH Hoekstra FW Steutel |
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Institution: | Eindhoven University of Technology Eindhoven, The Netherlands |
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Abstract: | We consider a Markov chain with a general state space, but whose behavior is governed by finite matrices. After a brief exposition of the basic properties of this chain, its convenience as a model is illustrated by three limit theorems. The ergodic theorem, the central limit theorem, and an extreme-value theorem are expressed in terms of dominant eigenvalues of finite matrices and proved by simple matrix theory. |
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