To give you a taste of why the Norris PDF is so valued, consider a typical exercise (paraphrased from Chapter 1, Exercise 1.8):
A particle moves on the vertices of a triangle. At each step, it moves to one of the other two vertices with equal probability. Let T be the time of first return to the starting vertex. Find the probability generating function of T.
Why this is hard for novices: Norris provides no hints. He assumes you know how to set up first-step analysis for generating functions. The solution requires solving a quadratic equation and distinguishing between aperiodic and periodic behavior. markov chains jr norris pdf
Why experts love it: The problem teaches you more than a whole chapter of a different textbook. It forces you to understand generating functions, hitting times, and state classification simultaneously.
If you can solve 70% of Norris’s exercises, you have mastered Markov chains at a Cambridge-level standard. If you have access to a university library,
James R. Norris is a Professor of Stochastic Analysis at the University of Cambridge. His research sits at the intersection of probability theory, analysis, and mathematical physics. However, his most famous contribution to the wider mathematical community is this 120-page powerhouse of a book.
Why "Markov Chains" (1997) stands out:
This is where Norris excels. The transition from discrete time (steps) to continuous time (Poisson processes) is notoriously difficult to teach.
Norris’s exposition shines in four critical proofs. If you find a partial PDF or lecture notes, prioritize: To give you a taste of why the