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.
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页码：741 / 758
页数：18
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