The spectral expansion solution method for Markov processes on lattice strips

A large class of two-dimensional Markov models, whose state space is a lattice strip, can be solved efficiently by means of spectral expansion. The equilibrium distribution of a stochastic process of this type is obtained in terms of the eigenvalues and eigenvectors of a certain matrix polynomial. This method is described in some detail, and examples of its application are presented. The relation between spectral expansion and other existing approaches, such as generating functions or the matrix-geometric method, is discussed. A few possible directions for further research are mentioned.