Numerical methods in Markov chain modeling
Résumé
This paper describes and compares several methods for computing stationary probability distributions of Markov chains. The main linear algebra problem consists of computing an eigenvector of a sparse, usually non-symmetric, matrix associated with a known eigenvalue. It can be also be cast as a problem of solving a homogeneous, singular linear system. We present several methods based on combinations of Krylov subspace techniques, single vector power iteration and relaxation procedures, and acceleration techniques. We compare the performance of these methods on some realistic problems.