Controlling rough paths

被引：354

作者：

Gubinelli, M ^{[1
]}

机构：

[1] Dipartimento Matemat Appl U Dini, I-56125 Pisa, Italy

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2004年 / 216卷 / 01期

关键词：

rough path theory; path-wise stochastic integration;

D O I：

10.1016/j.jfa.2004.01.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We formulate indefinite integration with respect to an irregular function as an algebraic problem which has a unique solution under some analytic constraints. This allows us to define a good notion of integral with respect to irregular paths with Holder exponent greater than 1/3 (e.g. samples of Brownian motion) and study the problem of the existence, uniqueness and continuity of solution of differential equations driven by such paths. We recover Young's theory of integration and the main results of Lyons' theory of rough paths in Holder topology. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：86 / 140

页数：55

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