Stochastic Complementation, Uncoupling Markov Chains, and the Theory of Nearly Reducible Systems 论文

摘要

. A concept called stochastic complementation is an idea which occurs naturally, although not always explicitly, in the theory and application of finite Markov chains. This paper brings this idea to the forefront with an explicit definition and a development of some of its properties. Applications of stochastic complementation are explored with respect to problems involving uncoupling procedures in the theory of Markov chains. Furthermore, the role of stochastic complementation in the development of the classical Simon--Ando theory of nearly reducible system is presented. Key words. Markov chains, stationary distributions, stochastic matrix, stochastic complementation, nearly reducible systems, Simon--Ando theory AMS(MOS) subject classifications. 65U05, 60-02, 60J10, 60J20, 15-02, 15A51, 90A14 1. Introduction. Although not always given an explicit name, a quantity which we shall refer to as a stochastic complement arises very naturally in the consideration of finite Markov chains. This...