On ergodic properties of homogeneous Markov chains

Golovneva E. V.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 1.

Abstract:
In this paper we continue our investigations initiated in [1]. Namely, we study the spectrum of Kolmogorov matrices with at least one column separated from zero. It is shown that \(\lambda=0\) is an eigenvalue with multiplicity 1, while the rest of the spectrum is separated from zero. Therefore, a Markov process generated by such a matrix converges to its uniquely defined final distribution exponentially fast. We give an explicit estimate for the rate of this convergence.

Keywords: Markov processes, generator, spectrum of a matrix, final projector

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