Stochastic B-series and order conditions for exponential integrators
arXiv:1801.020516 citationsh-index: 12
Originality Incremental advance
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Provides a theoretical foundation for analyzing the accuracy of exponential integrators in stochastic settings, which is important for numerical simulation of stiff SDEs.
The paper derives order conditions for stochastic exponential integrators applied to stiff stochastic differential equations, covering both Itô and Stratonovich calculus.
We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential integrators. Representing the exact and approximate solutions using B-series and rooted trees, we derive the order conditions for stochastic exponential integrators. The resulting general order theory covers both Itô and Stratonovich integration.