




















We have formulated higher-order integration by parts formulae on the path space restricted between two curves, with respect to pinned/ordinary Wiener measures. The higher-order integration by parts formulae introduce nontrivial boundary terms, unlike the first-order one. Furthermore, in the process of proving these formulae, it becomes necessary to employ the construction methods of Brownian excursion and Brownian house-moving through random walk approximations. To express the integration by parts formula concisely, we introduced a notation called Symmetrization. This notation enables the rewriting of the intricate expressions of boundary terms associated with higher-order integration by parts into more concise forms. Additionally, we provided a probabilistic explanation for the boundary terms by introducing symbols based on the concept of infinitesimal probability. These efforts are aimed at fostering an intuitive understanding of the integration by parts formulae.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。