On a two-level multigrid solution method for finite Markov chains Original Research Article

We study a two-level algebraic multigrid scheme for computing the stationary distribution of a homogeneous Markov chain with a finite state space. We reveal its relationship to an iterative aggregation-disaggregation method, provide an error analysis, and prove its local convergence. Moreover, we discuss the stochastic meaning of a block SOR procedure that can be used as iterative smoother of the multigrid scheme.