文章基本信息

标题：On Nonlinear Rough Paths
本地全文：下载
作者：David Nualart ; Panqiu Xia
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2020
卷号：17
期号：1
页码：545
DOI：10.30757/ALEA.v17-22
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：In this paper, we develop the theory of nonlinear rough paths. Following the ideas of Lyons and Gubinelli, we define the nonlinear rough integral ∫ t s W(dr, Yr), where W and Y are only α-Hölder continuous in time with α ∈ ( 1 3 , 1 2 ]. Also, we study the Kunita-type equation Yt = ξ ∫ t 0 W(dr, Ys), obtaining the local and global existence and uniqueness of the solution under suitable sufficient conditions. As an application, we study transport equations with rough vector fields and observe that the classical solution formula for smooth and Young’s cases does not provide a solution to the rough equation. Indeed this formula satisfies a transport equation with additional compensator terms (see (1.7)).
其他关键词：Nonlinear rough paths, controlled rough paths, nonlinear rough integrals, rough differential equations, Itô’s formula, rough partial differential equations.