Infinite horizon reflected backward stochastic differential equations with Markov chains

We first give the existence and uniqueness results for infinite horizon backward stochastic differential equations with Markov chains, taking advantage of the martingale representation theorem and fixed point principle. Then we prove the well-posedness results for infinite horizon reflected backward stochastic differential equations with Markov chains, by virtue of the Snell envelope theory and contraction mapping method. Comparison theorems for the above two kinds of equations are also obtained, via the linearization approach or properties of reflected backward stochastic differential equations, respectively.