Continuous-Time Markov Processes
Luca Leuzzi, Enzo Marinari, Giorgio Parisi · Cambridge University Press eBooks · 2025
Here we return to discrete Markov processes, but this time with continuous-time processes. We first consider, study, and solve specific examples such as Poisson processes, divergent birth processes, and birth-and-death processes. We derive the master equations for their probability distributions, and derive and discuss important solutions. In particular, we deepen the theory of Feller for divergent birth processes. In the end we formally study the general case of Markov processes in the stationary case, writing down the forward and the backward Kolmogorov master equations.