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DOI: 10.23671/VNC.2012.14.10952

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
Language: Russian Download the full text  
For citation: Golovneva E. V. On ergodic properties of homogeneous Markov chains.Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], 2012, vol. 14, no. 1, pp. 37-46. DOI 10.23671/VNC.2012.14.10952


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