Books on Markov processes, with emphasis on continuous-time

Question

Is there a comprehensive book on continuous-time Markov processes that doesn't completely focus on diffusions? I know the book of Liggett (Continuous Time Markov Processes), but find myself way too often looking things up that are not in that book. Markov Processes, Brownian Motion, and Time Symmetry by Kai Lai Chung is pretty inexpensive, but I have no experience with it. I realize this is a broad question, but I feel there is a gaping hole in my probability theory library.

Answer 1

In the book Brownian Motion, Martingales, and Stochastic Calculus by Le Gall, there is a chapter called "General Theory of Markov Processes." While the book is not about Markov processes, Le Gall mentions some references in the notes at the end of the book:

The reader interested in the more general theory of Markov processes may have a look at the classical books of Blumenthal and Getoor, Meyer, and Sharpe.

I have not read any of these books but I plan to give Sharpe's book a look, after I have finished with Le Gall's book.