粗糙路径的积分-截断变分法
Integration of rough paths - the truncated variation approach
摘要：
利用截断变分技巧，得到了粗糙路径驱动的黎曼-斯蒂尔切斯积分的Loeve-Young不等式的一个改进形式.这使我们能够加强一些结果的存在性积分方程的解决方案由中度不规则的信号。我们还介绍了一个新的巴拿赫空间，包含作为一个真子空间的路径有限$p$ -变化，并开发，在一个系统的方式，几个平行的结果，从这个空间的路径，迄今为止获得的路径有限$p$ -变化。本文首先给出了黎曼-斯蒂尔切斯积分存在性的一般定理。
英文摘要：
Using truncated variation techniques we obtain an improved version of the Loeve-Young inequality for the Riemann-Stieltjes integrals driven by rough paths. This allowed us to strenghten some result on the existence of solutions of integral equations driven by moderately irregular signals. We introduce also a new Banach space, containing as a proper subspace the paths with finite $p$-variation, and develop, in a systematic way, several parallel results for the paths from this space, obtained so far for the paths with finite $p$-variation. We start the paper with a general theorem on the existence of the Riemann-Stieltjes integral.
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。
