Time reversibility of random process

Random processes can be used to describe the evolution of a real systems over time. Discrete-time Markov chains are random processes that meet special assumptions, but they still have a lot of practical applications. Some chains have the property that it is impossible to tell if they are being observed when the passage of time is reversed. We call such chains time reversible. In this paper, we define a time reversible Markov chain with discrete time, we show how it can be verified that a given chain is time reversible, and we introduce basic properties and examples of time reversible chains. At the same time, we apply the knowledge of time reversibility to the problem of finding the stationary distribution of specific Markov chains.