Stochastic Partial Differential Equations: Theory and Numerics

This course introduces basic theory and numerics of stochastic partial differential equations (SPDEs). Topics include Brownian motion and stochastic calculus in Hilbert spaces, classification of SPDEs and solutions, stochastic elliptic, hyperbolic and parabolic equations, regularity of solutions, linear and nonlinear equations, analytic and numerical methods for SPDEs. Topics of particular interest will also be discussed upon agreements between the instructor and audience. All three courses APMA 2630 , APMA 2640 , APMA 2550 are background recommended but not required.