Gene Golub SIAM Summer School 2016
July 25 - August 5, 2016

Home>Courses   All the lectures and tutorial sections will take place in Randell Hall, Room 326.   Six short courses will be taught as traditional classroom-style lectures. There will also be a number of tutorial sessions in which students, together with an instructor, work out detailed example problems.      (1) Introduction to stochastic differential equations I                -- Brownian motion, martingales and stopping times, Markovian properties of Brownian motion           -- Ito and other versions of stochastic calculus           -- Stochastic differential equations (SDEs), O-U processs, Malliavin calculus      (2) Introduction to stochastic computation           -- Convergence and structural properties of integrators: Euler-Maruyama and Milstein methods           -- Metropolis algorithms for unbiased sampling and their application to SDEs      (3) Introduction to stochastic differential equations II           -- Randomly forced partial differential equations           -- Probability measures in infinite dimensions, rough path theory and regularity structures      (4) Stochastically forced Fluid equations           -- the effect of random forcing on partial differential equations from fluid dynamics           -- Navier-Stokes, Euler and other fluid models, ergodicity of solutions      (5) Invariant measures for dispersive equations           -- invariant measures for dynamical systems, Gibbs and Wiener measures           -- Schrodinger equations        (6) Introduction to stochastic homogenization           -- Methods for computing effective deterministic equations for PDEs with random coefficients           -- Multiscale expansion and cell problems, elliptic boundary value problems All lecture notes or related files can be found below: Nawaf Bow-Rabee David Nualart (Lecture 1, Lecture 2, Lecture 3) Gideon Simpson Xiaoming Song (Tutorial 1, Tutorial 2, Talk and the related paper)