标题： 关于随机变分原理 显示英文标题

标题： On Stochastic Variational Principles

摘要： 随机变分原理的研究涉及半鞅的固定端点和自适应变化构造的问题。 我们详细构建了半鞅的变化，这些变化不仅在确定性端点处固定，还在流形上的图首次进入时间和首次退出时间处固定。 我们在这些变化的背景下证明了变分法基本引理的随机版本。 利用这个框架，我们将随机哈密顿-庞特里亚金原理推广到任意噪声半鞅的局部坐标中。 对于相应的随机哈密顿-庞特里亚金原理的全局形式，我们通过限制于作为Stratonovich方程解的半鞅，引入了一种新的全局变分原理方法。 显示英文摘要

摘要： The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at deterministic endpoints, but also fixed at first entry times and first exit times for charts in a manifold. We prove a stochastic version of the fundamental lemma of calculus of variations in the context of these variations. Using this framework, we provide a generalization of the stochastic Hamilton-Pontryagin principle in local coordinates to arbitrary noise semimartingales. For the corresponding global form of the stochastic Hamilton-Pontryagin principle, we introduce a novel approach to global variational principles by restricting to semimartingales obtained as solutions of Stratonovich equations.