Markov chains in random environment with applications in queueing theory and machine learning
This provides theoretical foundations for analyzing stochastic processes in random environments, relevant for researchers in probability theory and applied fields like queueing and machine learning.
The authors proved the existence of limiting distributions for a broad class of Markov chains in random environments under drift and minorization conditions, establishing a law of large numbers for bounded functionals, with applications in queueing systems, machine learning algorithms, and autoregressive processes.
We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system dynamics should be contractive on the average with respect to the Lyapunov function and large enough small sets should exist with large enough minorization constants. We also establish that a law of large numbers holds for bounded functionals of the process. Applications to queuing systems, to machine learning algorithms and to autoregressive processes are presented.