Gamarnik — Advanced Stochastic Processes (MIT 15.070J, Fall 2013)
T1 — a graduate course published by mit-opencourseware under CC BY-NC-SA, taught by david-gamarnik and jointly listed by MIT's Sloan School of Management and EECS. Twenty-two lectures with notes.
What was read: the course description and the full lecture list, not all twenty-two note sets. The claims below are about what the course covers and in what order, which is the curriculum evidence this spoke collects — not about the contents of any individual proof.
The syllabus
The stated coverage is "measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems," with applications to finance, insurance, queueing and inventory.
The order is the surprise. It opens with metric spaces and topology, then spends five lectures on large deviations — i.i.d. rates, Cramér's theorem, applications, Gärtner-Ellis — before brownian-motion appears at lecture 6. Conditional expectation and filtration come at 9, martingales and stopping times at 10–11, concentration inequalities at 12–13, then four lectures on Itô calculus (14–17), integration with respect to martingales at 18, applications to financial economics at 19, and weak convergence and reflected Brownian motion to close.
Why this ordering is worth recording
It is a second route into the same subject, and it disagrees with the other two the spoke now holds about where to start.
wu-introduction-stochastic-processes starts from finite markov-chains and reaches martingales in its second half. lawler-stochastic-calculus starts from discrete-time martingales and reaches Brownian motion by taking limits of random walks. This course starts from topology and asymptotic rates — the probability of rare events — and treats Brownian motion as something to be handled once the analytic machinery is in place. Markov chains, the first thing in one course, are not a listed lecture topic here at all.
All three converge on Itô calculus, and two of the three end on finance. The subject has a destination the field agrees about and an entrance it does not.
Related
stochastic-processes · brownian-motion · martingale · stochastic-calculus · wu-introduction-stochastic-processes · lawler-stochastic-calculus · david-gamarnik · mit-opencourseware · probability-theory · mathematics · synthesis