On Forward and Backward Kolmogorov Equations for Pure Jump Markov Processes and Their Generalizations

Abstract

Theory of Probability &Its Applications, Volume 68, Issue 4, Page 643-656, February 2024.
In the present paper, we first give a survey of the forward and backward Kolmogorov equations for pure jump Markov processes with finite and countable state spaces, and then describe relevant results for the case of Markov processes with values in standard Borel spaces based on results of W. Feller and the authors of the present paper.