Numerical solution of stochastic differential equations
(D Downes and S Lucas)
The numerical solution of differential equations forced by a Weiner process
is a particularly difficult problem, due to the nondifferentiable nature of
the stochastic, or random, process involved.
The approximation of the Weiner process by its Karhunen-Loeve expansion is being investigated along with solving the much more amenable resultant differential equation.
Initial results indicate that a substantial number of realisations are required before the approximation error becomes apparent, and that the numerical implementation is substantially enhanced.