Convergence and stability of implicit runge-kutta methods for systems with multiplicative noise
- Cite this article as:
- Hernandez, D.B. & Spigler, R. BIT (1993) 33: 654. doi:10.1007/BF01990541
A class ofimplicit Runge-Kutta schemes for stochastic differential equations affected bymultiplicative Gaussian white noise is shown to be optimal with respect to global order of convergence in quadratic mean. A test equation is proposed in order to investigate the stability of discretization methods for systems of this kind. Herestability is intended in a truly probabilistic sense, as opposed to the recently introduced extension of A-stability to the stochastic context, given for systems with additive noise. Stability regions for the optimal class are also given.