Google’s original algorithm used a Markov chain to measure the importance of web pages.
A concise review of measure theory, convergence theorems, and generating functions—essential for readers who need a refresher.
: Introduction to optional stopping theorems using Markov chains.
For anyone serious about understanding the theoretical underpinning of random processes, J.R. Norris's Markov Chains is the gold standard.
Which are you working on? (e.g., hitting times, invariant distributions, continuous-time Q-matrices)
Mastering Stochastic Processes: A Guide to "Markov Chains" by J.R. Norris
Martingales, potential theory, and an introduction to Brownian motion. Practical Applications
Norris uses standard notation but with precision. Familiarize yourself with:
Norris’s proofs are famously elegant. Instead of just memorizing the theorems (like the Strong Markov Property), write out the proofs line-by-line to understand how conditioning on the present mathematically isolates the past from the future. Implement the Algorithms in Python or R
If you do not have institutional access, excellent open-access alternatives covering identical syllabi include Introduction to Stochastic Processes by Gregory Lawler or lecture notes from MIT OpenCourseWare. Conclusion