对称随机微分方程的约化、重构和斜积分解
Reduction, reconstruction, and skew-product decomposition of symmetric stochastic differential equations
摘要：
我们提出的对称随机微分方程的解决方案，类似于那些可用于常微分方程的减少和重建程序。此外，我们使用的局部切线-正常分解，对称群是适当的，在附近的任何一个点的开放和密集的主轨道类型的构造局部斜积分裂。本文的第一部分中介绍的一般方法，然后适用于哈密顿的情况下，这是研究与特别照顾，并说明了几个例子。汉密尔顿范畴值得单独研究，因为在这种情况下，对称性的存在意味着在大多数情况下存在守恒律，通过动量映射进行数学描述，在分析中应该考虑到这一点。
英文摘要：
We present reduction and reconstruction procedures for the solutions of symmetric stochastic differential equations, similar to those available for ordinary differential equations. Additionally, we use the local tangent-normal decomposition, available when the symmetry group is proper, to construct local skew-product splittings in a neighborhood of any point in the open and dense principal orbit type. The general methods introduced in the first part of the paper are then adapted to the Hamiltonian case, which is studied with special care and illustrated with several examples. The Hamiltonian category deserves a separate study since in that situation the presence of symmetries implies in most cases the existence of conservation laws, mathematically described via momentum maps, that should be taken into account in the analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
