Variable Length Memory Chains: Characterization of stationary probability measures

Cénac, Peggy; Chauvin, Brigitte; Noûs, Camille; Paccaut, Frédéric; Pouyanne, Nicolas

doi:10.3150/20-bej1299

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Variable Length Markov Chains Parsimonious Random Fields And...1

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“…The set τ g is sometimes assumed to be countable, which amounts to saying that g is piecewise constant on a countable number of cylinders. By using the combinatorial structure brought by the context tree, precise results on existence and uniqueness of g-measures (in some cases necessary and sufficient conditions) are obtained in [49] and [17], without requiring global continuity of g.…”

Section: Variable Length Markov Chains Parsimonious Random Fields And...mentioning

confidence: 99%

Markov and almost Markov properties in one, two or more directions

van Enter,

Ny,

Paccaut

2020

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In this review-type paper written at the occasion of the Oberwolfach workshop Onesided vs. Two-sided stochastic processes (february 22-29, 2020), we discuss and compare Markov properties and generalisations thereof in more directions, as well as weaker forms of conditional dependence, again either in one or more directions. In particular, we discuss in both contexts various extensions of Markov chains and Markov fields and their properties, such as g-measures, Variable Length Markov Chains, Variable Neighbourhood Markov Fields, Variable Neighbourhood (Parsimonious) Random Fields, and Generalized Gibbs Measures.

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Section: Variable Length Markov Chains Parsimonious Random Fields And...mentioning

confidence: 99%