Abstract

This talk discusses the design and development of numerical methods for solving stochastic differential equations. It is shown how certain order barriers can be overcome, and fixed stepsize numerical results are presented.

However, a fixed stepsize implementation is not always appropriate, and so a variable stepsize implementation is described. It is important to remain on the correct Brownian path, and the approach here allows complete flexibility in the choice of stepsize; also presented are the results obtained using Proportional Integral (PI) Control for choosing the stepsize.

A number of difficulties arise when the SDEs are non-commutative; a new style of method (suitable for non-commutative SDEs) that overcomes the order reduction suffered by other methods is presented, along with numerical results.