RETRACTED: Fixed point theorems and explicit estimates for convergence rates of continuous time Markov chains (Retracted Article)

In this paper we give Banach fixed point theorems and explicit estimates on the rates of convergence of the transition function to the stationary distribution for a class of exponential ergodic Markov chains. Our results are different from earlier estimates using coupling theory, and from estimates using stochastically monotone one. Our estimates show a noticeable improvement on existing results if Markov chains contain instantaneous states or nonconservative states. The proof uses existing results of discrete time Markov chains together with h-skeleton. At last, we apply this result, Ray-Knight compactification and Ito excursion theory to two examples: a class of singular Markov chains and Kolmogorov matrix.