This is the note of course MATH/STATS 526 Discrete Stochastic Process at University of Michigan. The course is taught at FA2023 by Professor Melih Iseri.
Separated by Midterm, the first part of the course focus on discrete time Markov Chain while the second part focus on continuous time Markov Chain. To introduce conditional expectation in a more mathematical way, professor Iseri spend some time on introducing measure theory, which is sometimes skipped in this course.
The note is taken in Chinese where the translation is somewhat made by myself, so there may exist some difference between concepts in the note and other Chinese textbooks.