Ergodicity and random dynamical systems for conservative SPDEs
Benjamin Fehrman, Benjamin Gess, and Rishabh S. Gvalani
TL;DR
This paper introduces a probabilistic framework for conservative SPDEs, establishing a random dynamical system and proving the existence, uniqueness, and mixing properties of invariant measures for the associated Markov process.
Contribution
It provides the first probabilistic construction of a random dynamical system for conservative SPDEs and analyzes their invariant measures and mixing behavior.
Findings
Probabilistic construction of a random dynamical system for conservative SPDEs
Existence and uniqueness of invariant measures established
Proved mixing properties of the associated Markov process
Abstract
The dynamics of the solutions to a class of conservative SPDEs are analysed from two perspectives: Firstly, a probabilistic construction of a corresponding random dynamical system is given for the first time. Secondly, the existence and uniqueness of invariant measures, as well as mixing for the associated Markov process is shown.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Stochastic processes and statistical mechanics · Mathematical Dynamics and Fractals