Fundamental Markov systems

2005/09/06 by Ivan Werner, Werner, Ivan
Computer Science · Mathematics · #Algorithms and Data Compression #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #math.DS #math.PR

paper · pdf · doi:10.48550/arxiv.math/0509120

Added a conjecture

openalex publication_date 2005/09/06 · arxiv created 2009/02/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue development of the theory of Markov systems initiated in \citeWer1. In this paper, we introduce fundamental Markov systems associated with random dynamical systems and show that the proof of the uniqueness and empiricalness of the stationary initial distribution of the random dynamical system reduces to that for the fundamental Markov system associated with it. The stability criteria for the latter are much clearer.

Citations

• On coding with Feller contractive Markov systems

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• Ergodicity and random dynamical systems for conservative SPDEs