Reversible Markov kernels and involutions on product spaces
Copyright policy )Reversible Markov kernels and involutions on product spaces
In this paper the relations between independence preserving (IP) involutions and reversible Markov kernels are investigated. We introduce an involutive augmentation H = (f, g_f) of a measurable function f and relate the IP property of H to f-generated reversible Markov kernels. Various examples appeared in the literature are presented as particular cases of the construction. In particular, we prove that the IP property generated by the (reversible) Markov kernel of random walk with a reflecting barrier at the origin characterizes geometric-type laws
14 pages
independence preserving maps, Stationary stochastic processes, involutions, Characterization and structure theory of statistical distributions, Probability (math.PR), FOS: Mathematics, Probability distributions: general theory, reversible Markov chains, Markov chains (discrete-time Markov processes on discrete state spaces), Burke's property, Mathematics - Probability, 60J05, 60G10, 60E05, 62E10
independence preserving maps, Stationary stochastic processes, involutions, Characterization and structure theory of statistical distributions, Probability (math.PR), FOS: Mathematics, Probability distributions: general theory, reversible Markov chains, Markov chains (discrete-time Markov processes on discrete state spaces), Burke's property, Mathematics - Probability, 60J05, 60G10, 60E05, 62E10
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