In the study of stochastic models, our works focus on setting up a unified theoretic framwwork through using the RG-factorizations of, such as, Markov processes, Markov reward processes, Markov decision processes, stochastic games, evolutionary game and so forth.  See Li's 2010 book: Constructive Computation in Stochastic Models with Applications: The RG-Factorizations. For the RG-factorizations, an interesting generalization with useful remarks was given by  V. Vigon (2013):  LU-Factorization Versus Wiener-Hopf Factorization for Markov Chains.

The RG-factorizations play an important role in performance evaluation, optimization and decision for many practical stochastic systems. Using the RG-factorizations, we gave several general results including the R-measure expression for the stationary probability vector, two types of expressions for the quasi-stationary probability vector, the solution to the Poisson equations, numerical methods for Markov processes, stochastic games and evolutionary games. When applying general Markov processes, the RG-factorizations show a stronger applicable performance, for example, dealing with retrial queues, processor-sharing queues, fluid queues, matched queues; and computer networks, manufacturing systems and so forth.