Norris Markov Chains 2021 -

Norris is a master of concise, precise exposition. Proofs are tight but complete. The book doesn’t cut corners. For example, the treatment of the classification of states (recurrence/transience, periodicity) is arguably the cleanest in any textbook.

At ~250 pages, it covers exactly what you need (discrete time, continuous time, and applications to Brownian motion/CTRWs) without bloat. You can read it cover-to-cover in a semester. norris markov chains

Sheldon Ross’s Probability Models gives dozens of real-world business/engineering examples. Norris gives mathematical examples (e.g., simple random walk, branching processes, birth-death chains). He rarely spells out "this is how you model a call center." Norris is a master of concise, precise exposition

In the study of probability theory, few texts are as widely cited and respected as Markov Chains by J.R. Norris (Cambridge University Press, 1997). Serving as a cornerstone of the Cambridge Series in Statistical and Probabilistic Mathematics , this book is the definitive guide for students and researchers bridging the gap between elementary probability and advanced stochastic processes. For example, the treatment of the classification of

def simulate(self, initial_state, steps): current_state = initial_state print(f"Initial State: current_state") for _ in range(steps): current_state = self.next_state(current_state) print(f"Next State: current_state")