Quasi-compactness and absolutely continuous kernels, applications to Markov chains

Details Quasi-compactness and absolutely continuous kernels, applications to Markov chains Quasi-compactness and absolutely continuous kernels, applications to Markov chains

2006-06-27

arxiv.org/abs/math/0606680v1

Mathematics

Probability

31 pages

Scientific paper

We show how the essential spectral radius of a bounded positive kernel, acting on bounded functions, is linked to its lower approximation by certain absolutely continuous kernels. The standart Doeblin's condition can be interpreted in this context, and, when suitably reformulated, it leads to a formula for the essential spectral radius. This results may be used to characterize the Markov kernels having a quasi-compact action on a space of measurable functions bounded with respect to some test function, when no irreducibilty and aperiodicity are assumed.

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