Mixing properties of some Markov chains models in random environments

2025/09/19 by Attila Lovas, Lovas, Attila, Lionel Truquet +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2509.16118

openalex publication_date 2025/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Markov chains in random environments (MCREs) have recently attracted renewed interest, as these processes naturally arise in many applications, such as econometrics and machine learning. Although specific asymptotic results, such as the law of the large numbers and central limit theorems, have been obtained for some of these models, their annealed dependence properties, such as strong mixing properties, are not well understood in general. We derive strong mixing properties for a wide range of MCREs that satisfy some drift/small set conditions, with general assumptions on the corresponding stochastic parameters and the mixing properties of the environments. We then demonstrate the wide range of applications of our results in time series analysis and stochastic gradient Langevin dynamics, with fewer restrictions than those found in existing literature.

Citations

• Transition of α-mixing in Random Iterations with Applications in Queuing Theory
• Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics
• Strong mixing properties of discrete-valued time series with exogenous covariates
• Ergodic properties of some Markov chains models in random environments
• On the stability of the stochastic gradient Langevin algorithm with\n dependent data stream
• Stationarity and ergodic properties for some observation-driven models in random environments
• Ergodic theorems for queuing systems with dependent inter-arrival times
• Markov chains in random environment with applications in queueing theory\n and machine learning
• On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex case
• On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case
• On the ergodicity of certain Markov chains in random environments
• Non-convex learning via Stochastic Gradient Langevin Dynamics: a\n nonasymptotic analysis
• A Bernstein type inequality and moderate deviations for weakly dependent sequences

Cited by

• Sharp Mixing Rates for Markov Chains on General Spaces with Unbounded Random Environments

Related

• Sharp Mixing Rates for Markov Chains on General Spaces with Unbounded Random Environments
• Transition of α-mixing in Random Iterations with Applications in Queuing Theory
• Random Walks on Dynamical Random Environments with Non-Uniform Mixing
• On the Markov chain central limit theorem
• Statistical properties for mixing Markov chains with applications to dynamical systems