DIFFERENTIAL EQUATIONS DRIVEN BY Π-ROUGH PATHS

被引：7

作者：

Gyurko, Lajos Gergely ^{[1
,2
]}

机构：

[1] Univ Oxford, Math Inst, Andrew Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

[2] Univ Oxford, Oxford Man Inst Quantitat Finance, Eagle House,Walton Well Rd, Oxford OX6 2ED, England

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2016年 / 59卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

rough paths; differential equations; stochastic integrals; stochastic differential equations; STOCHASTIC-ANALYSIS; SIGNALS;

D O I：

10.1017/S0013091515000474

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper revisits the concept of rough paths of inhomogeneous degree of smoothness (geometric Pi-rough paths in our terminology) sketched by Lyons in 1998. Although geometric Pi-rough paths can be treated as p-rough paths for a sufficiently large p, and the theory of integration of Lip(gamma) one-forms (gamma > p - 1) along geometric p-rough paths applies, we prove the existence of integrals of one-forms under weaker conditions. Moreover, we consider differential equations driven by geometric Pi-rough paths and give sufficient conditions for existence and uniqueness of solution.

引用

页码：741 / 758

页数：18

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