Markov Processes & Diffusion: Textbook Reference

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eXorikos
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This semester I have a course on mathematical methods in physics. It's in three parts and the first professor is talking about Markov processes (discrete and continuous time) and diffusion. The problem is he doesn't have any notes or a reference textbook.

Do you know any textbook on these topics?
 
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Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, 2nd Edition

That's the one we use at my school; it's pretty friendly.