Homework 1 is assigned, due by the end of the day on February 9
The lecture notes are available here; they will be updated and revised throughout the semester.
Welcome! Watch this space for all important course-related announcements.
I will be away during the first week of the semester. Link to a video recording of Lecture 1 is available here.
About this course
What is this?
Stochastic Differential Equations in Optimization, Control, and Learning is an advanced graduate course introducing theory and engineering applications of stochastic differential equations. The following fundamental topics will be covered: Brownian motion and diffusion processes; forward Kolmogorov (Fokker-Planck) and backward Kolmogorov equations; stochastic integrals of Itô and Stratonovich; change of measure (Cameron-Martin-Girsanov theory); and the Feynman-Kac formula. The theoretical concepts will be illustrated and developed through applications to stochastic control (the Kalman-Bucy filter and the LQG problem, nonlinear filters, Hamilton-Jacobi-Bellman equation for controlled diffusions), optimization (Langevin dynamics and simulated annealing in continuous time), and machine learning (sampling via the Schrödinger bridge and score-based generative models). Prerequisites include probability and random processes, multivariable calculus, and linear algebra. Other material and background will be introduced as needed.
There is no official textbook. The material in this course will be based on a number of sources, including:
W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control, Springer, 1975
E. Wong and B. Hajek, Stochastic Processes in Engineering Systems, Springer, 1985
J. Michael Steele, Stochastic Calculus and Financial Applications, Springer, 2001
G.A. Pavliotis, Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations, Springer, 2014
W. E, T. Li, and E. Vanden-Eijnden, Applied Stochastic Analysis, American Mathematical Society, 2019
Additional readings and instructor's course notes will be provided during the semester.
Grades will be based on homework (60%) and a written report (40%).