In many modelling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic differential equation. However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for stochastic differential equations (SDEs) are much less sophisticated.

This seminar will show how B-series can be used to study the order conditions of numerical methods for SDEs in a very general manner. Both local order and global order convergence results will be established and results given to illustrate these theoretical results. This places the design of numerical methods for SDEs on the same footing as the deterministic case and should lead to significant developments in the area.

MINISIMPOSIUM SESSION: 7. Numerical methods for Stochastic equations