论文标题
外来的B系列和S系列：代数结构和不变测量采样的顺序条件
Exotic B-series and S-series: algebraic structures and order conditions for invariant measure sampling
论文作者
论文摘要
B系列和概括是分析数值集成商的强大工具。引入了一个名为Exotic芳香B系列的延伸，以研究对Ergodic SDE的不变度度量进行采样的顺序条件。引入了新的对称归一化系数，我们分析了与外来B系列和S系列有关的代数结构。确切地说，我们证明了格罗斯曼·拉尔森（Grossman-Larson）代数与外来森林和嫁接森林的关系与康纳斯 - 肯特（Connes-Kreimer）煤层的相应二元组之间的关系，并使用它来研究有关外来S系列的天然组成法。将此代数框架应用于一类随机runge-kutta方法的订单条件的推导，我们提出了一个乘法属性，可确保自动满足某些订单条件。
B-series and generalizations are a powerful tool for the analysis of numerical integrators. An extension named exotic aromatic B-series was introduced to study the order conditions for sampling the invariant measure of ergodic SDEs. Introducing a new symmetry normalization coefficient, we analyze the algebraic structures related to exotic B-series and S-series. Precisely, we prove the relationship between the Grossman-Larson algebras over exotic and grafted forests and the corresponding duals to the Connes-Kreimer coalgebras and use it to study the natural composition laws on exotic S-series. Applying this algebraic framework to the derivation of order conditions for a class of stochastic Runge-Kutta methods, we present a multiplicative property that ensures some order conditions to be satisfied automatically.
