The first part of this course serves as an introduction to stochastic calculus and stochastic differential equations. It will define rigorously the notion of a differential equation driven by noise, and show how to manipulate such equations. These models have a wide range of applications in machine learning, stochastic control, inference, and networks. The second part discusses applications of these methods to solve problems in stochastic control theory, optimal stochastic control with complete as well as partial observations, linear and nonlinear filtering theory, optimal stopping, impulse controls, Markov chain Monte Carlo methods, and diffusion approximations for Multi Armed bandits.
Grading:
Class participation, Midterm exam and End-term project.
References:
Lecture notes on Stochastic Calculus, Filtering, and Stochastic Control by Ramon Van Handel.