Equivalence–Singularity Dichotomy in Markov Measures
Copyright policy )Equivalence–Singularity Dichotomy in Markov Measures
We establish an equivalence-singularity dichotomy for a large class of one-dimensional Markov measures. Our approach is new in that we deal with one-sided and two-sided chains simultaneously, and in that we do not appeal to any 0-1 law. In fact we deduce a new 0-1 law from the dichotomy.
16 pages
Measures and integrals in product spaces, Markov chains, 60J10, 28A35, 60F20, Probability (math.PR), FOS: Mathematics, Markov fields, Kakutani dichotomy, Zero-one laws, Markov chains (discrete-time Markov processes on discrete state spaces), Mathematics - Probability, zero-one law
Measures and integrals in product spaces, Markov chains, 60J10, 28A35, 60F20, Probability (math.PR), FOS: Mathematics, Markov fields, Kakutani dichotomy, Zero-one laws, Markov chains (discrete-time Markov processes on discrete state spaces), Mathematics - Probability, zero-one law
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