Poisson's equation for Markov chains: bounds and monotonicity


In this talk, we will present some recent results on Poisson's equation for Markov chains. For irreducible and positive recurrent discrete-time Markov chains, we will consider analytical bounds for solutions of Poisson's equation. The bounds are further applied to derive the truncation approximation bounds for the stationary distribution, the bounds on the variance constant, and the error bounds on the difference betwen the empirical average and its limit value. We also consider the block monotonicity for a solution of Poisson's equation, which may be used to investigate matrix-analytical queuing models.