Wu — Introduction to Stochastic Processes (MIT 18.445, Spring 2015)
T1 — an MIT Department of Mathematics course published by mit-opencourseware under CC BY-NC-SA, taught by Dr. Hao Wu (hao-wu). Twenty-four lectures with notes; listed as graduate, and prerequisites are only "basic knowledge in probability theory and linear algebra, including conditional expectation and matrix operations."
What was read: the course description, prerequisites and full lecture list, not the individual lecture notes. The claims here are about the shape of the syllabus.
The syllabus
Its own one-line description — "an introduction to Markov chains, random walks, martingales, and Galton-Watsom tree" — undersells the weighting. Thirteen of the twenty-four lectures are markov-chains and random walks: finite chains, stationary distributions, time-reversal, then five lectures on mixing times (stationary times, lower bounds), random walk on networks, hitting times, and countable state spaces.
Only after the midterm does it reach conditional expectation and martingales (15–18: optional stopping, convergence, uniform integrability), the Galton-Watson branching tree, the Poisson process, and continuous-time Markov chains with their infinitesimal generator, recurrence and stationary distribution.
What it is and is not
There is no brownian-motion, no stochastic integral and no finance here. That is the finding worth keeping: an entire graduate course on stochastic-processes that never leaves the discrete and jump-driven side of the subject, sitting beside gamarnik-advanced-stochastic-processes at the same institution, in the same era, which never mentions Markov chains as a lecture topic.
The prerequisite line is the other half of it. Conditional expectation and matrix operations are enough to start, and matrices are enough because a finite Markov chain is a matrix — which makes this the point where linear-algebra becomes the working tool of probability rather than a neighbouring subject.
Related
stochastic-processes · markov-chain · martingale · probability-theory · linear-algebra · gamarnik-advanced-stochastic-processes · lawler-stochastic-calculus · hao-wu · mit-opencourseware · mathematics · synthesis