Comment on "Numerical methods for stochastic differential equations".
Wilkie [Phys. Rev. E 70, 017701 (2004)] used a heuristic approach to derive Runge-Kutta-based numerical methods for stochastic differential equations based on methods used for solving ordinary differential equations. The aim was to follow solution paths with high order. We point out that this approach is invalid in the general case and does not lead to high order methods. We warn readers against the inappropriate use of deterministic calculus in a stochastic setting.
Burrage
Kevin
K
Advanced Computational Modelling Centre, University of Queensland, Brisbane QLD 4072, Australia.
Burrage
Pamela
P
Higham
Desmond J
DJ
Kloeden
Peter E
PE
Platen
Eckhard
E