On Discrete Time Reversibility modulo State Renaming and its Applications

Time reversibility plays an important role in the analysis of continuous and discrete time Markov chains (DTMCs). Specifically, the computation of the stationary distribution of a reversible Markov chain has been proved to be very efficient and does not require the solution of the system of global balance equations. A DTMC is reversible when the processes at forward and reversed time are probabilistically indistinguishable. In this paper we introduce the concept of ρ-reversibility, i.e., a notion of reversibility modulo a renaming of the states, and we contrast it with the previous definition of dynamic reversibility especially with respect to the assumptions on the state renaming function. We also discuss the applications of discrete time reversibility in the embedded and uniformized chains of continuous time processes.