Order Conditions of Stochastic Runge-Kutta Methods by B-Series

@article{Burrage2000OrderCO,
  title={Order Conditions of Stochastic Runge-Kutta Methods by B-Series},
  author={Kevin Burrage and Pamela M. Burrage},
  journal={SIAM J. Numerical Analysis},
  year={2000},
  volume={38},
  pages={1626-1646}
}
In this paper, general order conditions and a global convergence proof are given for stochastic Runge–Kutta methods applied to stochastic ordinary differential equations (SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to… CONTINUE READING
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