Advanced Stochastic Processes
A graduate level treatment of stochastic processes from MIT, covering measure theoretic probability, martingales, filtration and stopping theorems, and elements of large deviations theory. The course builds up Brownian motion and reflected Brownian motion, then develops stochastic integration and Ito calculus along with functional limit theorems. Applications tie the mathematics to finance theory, insurance, queueing systems and inventory models, showing how the abstract machinery gets used in practice. Materials come from MIT OpenCourseWare and include lecture notes and problem sets from the Sloan School of Management and the Electrical Engineering and Computer Science department, free to access under a Creative Commons license. The course assumes prior exposure to probability and is pitched at students who already have a foundation in measure theory or are ready to acquire one alongside the material.