Tips on good literature regarding Markov chains and processes

Question

I have read a course in Markov processes at my uni (Im a graduate student in Lund, Sweden) and would like to dig a bit deeper into the field. The book provided for that course was written in by a professor in Swedish and is way too elementary for my taste.

To give you an idea of which level I am interested in I have read several other courses in inference theory, time series and probability theory so I am not completely new in the subject. I am also trying to learn more about measure theory to be able to dig deeper in the field.

Do you have any tips on good literature concerning Markov chains and processes?

Answer 1

For a basic introduction (so basic they might be below you), you might want to try

An Introduction to Stochastic Modeling (Karlin and Taylor).

Or

Stochastic Processes (Ross).

Then there is

A First Course in Stochastic Processes (also Karlin and Taylor).

and

A Second Course in Stochastic Processes (also Karlin and Taylor).

Another introduction that is a bit more in depth introduction is given by Stroock called

An Introduction to Markov Processes.

There are also tons of books on more specialized topics, but those should be a good base I think.