About: Kolmogorov equations (continuous-time Markov chains)

In mathematics and statistics, in the context of Markov processes, the Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, are a pair of systems of differential equations that describe the time evolution of the process's distribution. This article, as opposed to the article titled Kolmogorov equations, focuses on the scenario where we have a continuous-time Markov chain (so the state space is countable). In this case, we can treat the Kolmogorov equations as a way to describe the probability , where (the state space) and are the final and initial times, respectively.