2020/11/30 by Aernout C. D. van Enter, van Enter, Aernout, Arnaud Le Ny +3
Mathematics · #60K35 #82B20 #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.2011.14664
openalex publication_date 2020/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.