A variation embedding theorem and applications

被引：37

作者：

Friz, Peter ^{[1
]}

Victoir, Nicolas ^{[1
]}

机构：

[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB2 1TN, England

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2006年 / 239卷 / 02期

关键词：

fractional Sobolev; Besov spaces; q-variation embedding; rough paths; regularity of the Ito-map; regularity of Cameron-Martin;

D O I：

10.1016/j.jfa.2005.12.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Fractional Sobolev spaces, also known as Besov or Slobodetski spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces. Applications include a new route to a regularity result by Kusuoka for stochastic differential equations, integration against Besov-paths, a regularity criterion for rough paths and a new regularity result for Cameron-Martin paths associated to fractional Brownian motion. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：631 / 637

页数：7

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