Stochastic B-Series and Order Conditions for Exponential Integrators
We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential Runge–Kutta integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential Runge–Kutta integrators. The resulting general order theory covers both Itô and Stratonovich integration.
- 9.G.N. Milstein, Numerical Integration of Stochastic Differential Equations. Mathematics and Its Applications, vol. 313 (Kluwer Academic Publishers Group, Dordrecht, 1995). Translated and revised from the 1988 Russian originalGoogle Scholar