Schwarz methods for quasi stationary distributions of Markov chains

We study computational schemes for quasi stationary distributions of Markov chains, having matrices which are quasi stochastic, i.e., all of their row sums are less than or equal to one. We develop Schwarz methods for the corresponding distributions. In particular, we get the semiconvergence of additive and multiplicative Schwarz methods, and that of two level Schwarz iterative methods for the quasi stationary distributions (QSDs). We provide two examples of Markov chains with QSDs, to explain our methods.