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

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

In this review-type paper written at the occasion of the Oberwolfach workshop {\em One-sided 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 e...

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Veröffentlicht in:Markov processes and related fields 2021-01, Vol.27 (3), p.315-338
Hauptverfasser: van Enter, Aernout, Ny, Arnaud Le, Paccaut, Frédéric
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Mathematics - Dynamical Systems
Mathematics - Probability
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Ny, Arnaud Le
Paccaut, Frédéric
description In this review-type paper written at the occasion of the Oberwolfach workshop {\em One-sided 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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Mathematics - Probability
title Markov and almost Markov properties in one, two or more directions
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