Numerical evaluation of Wiener integrals

Abstract

A systematic study of quadrature formulae for the Wiener integral ∫ F [ x ] w ( d x ) \int {F[x]w(dx)} of the type ∫ F [ θ ( u , ⋅ ) ] ν ( d u ) \int {F[\theta (u, \cdot )]\nu (du)} is presented. The Cameron and Vladimirov quadrature formulae, which are the function space analogues of Simpson’s Rule, are shown to fit into this framework. Numerical results are included.