Limit theorems for a Markov model of autoregulated gene expression

The main goal of this paper is to establish a criterion on the exponential ergodicity in the bounded Lipschitz distance, the strong law of large numbers (SLLN) and the central limit theorem (CLT) for a certain class of Markov chains, taking values in a Polish space. The examined dynamical systems provide a mathematical framework for modelling the stochastic dynamics of single-gene autoregulation in bacterium.The main goal of this paper is to establish a criterion on the exponential ergodicity in the bounded Lipschitz distance, the strong law of large numbers (SLLN) and the central limit theorem (CLT) for a certain class of Markov chains, taking values in a Polish space. The examined dynamical systems provide a mathematical framework for modelling the stochastic dynamics of single-gene autoregulation in bacterium.