On stationary Markov chains and independent random variables

Two new proofs are given for the fact that a stationary, irreducible, aperiodic Markov chain ( X n n = …, −1,0,1,2…) with denumerable state space has a representation of the form X′ n=g(U n−1, U n−2,…) , where g is a measurable function, ( U n , n= …, −1,0,1,2,…) a sequence of independent random var...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 34; no. 1; pp. 19 - 24
Main Authors Brandt, A., Lisek, B., Nerman, O.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.02.1990
Elsevier Science
Elsevier
SeriesStochastic Processes and their Applications
Subjects
Exact sciences and technology
i.i.d. random variables
Markov chain
Markov chain representation i.i.d. random variables
Markov processes
Mathematics
Probability and statistics
Probability theory and stochastic processes
representation
Sciences and techniques of general use
Markov chain
i.i.d. random variables
representation
Probability law
Uniform distribution
Measurable function
Stationary process
Representation
Random variable sequence
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Summary:Two new proofs are given for the fact that a stationary, irreducible, aperiodic Markov chain ( X n n = …, −1,0,1,2…) with denumerable state space has a representation of the form X′ n=g(U n−1, U n−2,…) , where g is a measurable function, ( U n , n= …, −1,0,1,2,…) a sequence of independent random variables uniformly distributed on (0,1), and ( X′ n ) has the same probability law as ( X n ).
ISSN:0304-4149
1879-209X
DOI:10.1016/0304-4149(90)90053-U