MATH-330: Martingales and Brownian motionIntroduction to the theory of discrete-time martingales including, in particular, the convergence and stopping time theorems. Application to branching processes. Introduction to Brownian motion and st
MATH-431: Theory of stochastic calculusIntroduction to the mathematical theory of stochastic calculus: construction of stochastic Ito integral, proof of Ito formula, introduction to stochastic differential equations, Girsanov theorem and F
PHYS-436: Statistical physics IVNoise and fluctuations play a crucial role in science and technology. This course treats stochastic methods, applying them to both classical problems and quantum systems. It emphasizes the frameworks
MATH-519: Topics in high-dimensional probabilityThis is a theoretical course about probability in high dimensions. We will look at some mathematical phenomena appearing as the number of random variables grows large - e.g. concentration of measure o
FIN-415: Probability and stochastic calculusThis course gives an introduction to probability theory and stochastic calculus in discrete and continuous time. The fundamental notions and techniques introduced in this course have many applicatio
EE-726: Sparse stochastic processesWe cover the theory and applications of sparse stochastic processes (SSP). SSP are solutions of differential equations driven by non-Gaussian innovations. They admit a parsimonious representation in a
MATH-615: Gaussian free field through random walksIn this lecture series some important objects of random geometry are introduced and studied. In particular, the relation between the Gaussian free field and random walks / Brownian motions is explored