Singular boundaries in the forward Chapman-Kolmogorov differential equation (Q1047139)

The authors address the derivation of the forward Chapman-Kolmogorov differential equation for the time evolution of the conditional transition probability of a Markov process in continuous time. They refer to the derivation of the equation given by [\textit{C. W. Gardiner}, Handbook of stochastic methods for physics, chemistry and the natural sciences. Springer Series in Synergetics, 13. Berlin etc.: Springer-Verlag., (1985; Zbl 0713.60076)], extending it to consider surface integrals, which have been neglected in the original derivation and which could lead to singularities at the boundaries of the phase-space domain.