Problem of Kolmogorov for Markovian chains
Marijus Jūris Mikalauskas
Vilniaus universitetas
Published 2008-12-21


Markovian chain
problem of Kolmogorov
asymptotical expansion
metrics of variation

How to Cite

Mikalauskas M. J. (2008) “Problem of Kolmogorov for Markovian chains”, Lietuvos matematikos rinkinys, 48(proc. LMS), pp. 407–411. doi: 10.15388/LMR.2008.18150.


The sums of random variables from two-state Markovian chain in the schemes of series are investigated. The sums are approximated by parametrical set of measures, which is constituted by all possible limit
measures of such sums, after making discrete in continuous cases. The problem of Kolmogorov is under solution: the accuracy of approximation by the most relevant measure from parametrical set is evaluated in
terms of metrics of variation. The common solution scheme of Kolmogorovæs problem is described and the final results for one particular parametrical measure are presented.

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