Research in Stochastic Differential Equations
Stochastic Differential Equations (SDEs) appear in many areas of science and engineering. SDEs are like ordinary differential equations with an additional random forcing term, usually white noise. Two of the best known examples are Geometric Brownian Motion, a simple and commonly used model for the evolution of stock prices, and the Langevin equation, a model of a molecular system especially in thermal equilibrium.
The School of Mathematics at the University of Manchester has a large group working on stochastic differential equations and related topics. Research on uncertainty quantification concerns differential equations with random data and focuses on developing fast and robust numerical methods for the Galerkin method. The groups on stochastic analysis and stochastic calculus investigate the underlying probability theory and there is an active group on mathematical finance.
Recent work on the numerical analysis of SDEs includes
- ergodic theory and the study of long time behaviour of numerical approximations of SDEs,
- analysis of algorithms for stochastic PDEs by Hilbert space theory,
- numerical methods for dissipative particle dynamics, stochastic delay differential equations, and stochastic PDE models of excitable media,
- software development in collaboration with NAG featuring state of the art algorithms for stochastic and random differential equations.
Members of staff involved