I would like know whether there is some kind of central limit theorem for time inhomogeneous Markov processes with continuous time and state space.
R. Dobrushin proved in his thesis (A) an important central limit theorem for Markov chains in discrete time and general state space that are not necessarily homogeneous in time. But I cannot find a continuous time version in the literature.
Any help in the form of a direct answer or a reference suggestion would be highly appreciated.
(A) Dobrushin, R. Central limit theorems for non-stationary Markov chains I,II. Theory of Probab. and its Appl. 1 65-80 (1956), 329-383.