How do you self - study advanced Markov chains?

Diving deeper into advanced Markov chains can be challenging without formal coursework, but a structured approach helps. First, make sure you have a solid grasp of the basics by revisiting foundational topics such as transition matrices, state spaces, and Markov property. The notes from San José State University by Dr. Guangliang Chen provided me with clear mathematical explanations that were very helpful. Next, supplement your reading with high-quality video tutorials. I found the ‘Markov Chains Clearly Explained’ series valuable for visually connecting theory with examples, especially when they cover computation of steady-state distributions and classification of states. Try to solve practice problems from stochastic process syllabi commonly used in B.Tech courses, focusing on exercises involving self-similar Markov processes and continuous-time chains. Websites offering open courseware on these topics can be a good resource. Joining online forums or social communities interested in stochastic processes is another great tip. Discussing problems with peers or experts helped me understand different perspectives and practical applications. Lastly, revisit the mathematical rigor behind Markov chain theorems as covered by authors like Norris. Reading research papers or advanced textbooks once you’re comfortable with intermediate materials can deepen your insight. Remember to pace your learning and regularly summarize what you’ve understood in your own words or notes. This active engagement boosted my retention and helped me tackle complex concepts more confidently.