标题： 一种粗糙路径方法用于类似Föllmer的路径积分 显示英文标题

标题： A rough path approach to pathwise stochastic integration à la Föllmer

摘要： 我们开发了一个路径随机积分的一般框架，该框架扩展了Föllmer的经典方法，超越了梯度类型被积函数和标准左点黎曼和，并提供了Itô、Stratonovich和反向Itô积分的路径对应物。 更准确地说，对于一个连续路径，在固定分划序列上同时具有二次变差和Lévy面积，我们定义路径随机积分为一般黎曼和的极限，并证明它们与相对于适当粗糙路径定义的积分一致。 此外，我们确定了在何种必要且充分条件下，连续路径的二次变差和Lévy面积相对于分划序列的选择是不变的。 显示英文摘要

摘要： We develop a general framework for pathwise stochastic integration that extends F\"ollmer's classical approach beyond gradient-type integrands and standard left-point Riemann sums and provides pathwise counterparts of It\^o, Stratonovich, and backward It\^o integration. More precisely, for a continuous path admitting both quadratic variation and L\'evy area along a fixed sequence of partitions, we define pathwise stochastic integrals as limits of general Riemann sums and prove that they coincide with integrals defined with respect to suitable rough paths. Furthermore, we identify necessary and sufficient conditions under which the quadratic variation and the L\'evy area of a continuous path are invariant with respect to the choice of partition sequences.