Stochastic PDE

Randomness plays an essential role in a diverse collection of phenomenon, such as the growth of a forest fire or a colony of bacteria, the spread of a disease and behavior of crowds, and the behavior of financial markets.  While the macroscopic or large-scale behavior of these systems is often time deterministic and described by the solution to an ordinary differential equation, the microscopic behavior and the fluctuations of these systems about their large-scale limits is effectively random.

These are described by partial differential equations with random noise, or stochastic partial differential equations.  Since the noise is highly irregular it is necessary to develop new techniques in order to understand the solutions. These typically blend elements from probability and analysis, and rely on Ito-Calculus in infinite dimensions, rough path theory, and renormalization.

Faculty: José A. Carrillo and Gui-Qiang G Chen

Postdoctoral Fellows: 

DPhil Students: Chin Ching Yeung