On the general transformation of Markov chains

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Soumia Benbakreti, Abderrahmane Yousfate

Abstract

In this work, we consider a class of homogeneous irreducible discrete states Markov process  ,  taking values in a partition of some topological space  . Using  a notion of fractional state,  we introduce a general transformation   such that      remains a Markov process. This general transformation includes also lumpability. Infinite kinds of this expanded Markov chain    can be constructed, however lumped  Markov chains are finite or may not exist .


Using general transformation   and fractional states, we give a necessary and sufficient condition under which the transformed process   remains still a Markov chain

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How to Cite
Soumia Benbakreti, Abderrahmane Yousfate. (2022). On the general transformation of Markov chains . Turkish Journal of Computer and Mathematics Education (TURCOMAT), 13(03), 1017–1033. https://doi.org/10.17762/turcomat.v13i03.13246
Section
Research Articles