Journal of the Mathematical Society of Japan

The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations

Terry J. LYONS and Danyu YANG

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Abstract

We give an overview of the recent approach to the integration of rough paths that reduces the problem to an inhomogeneous analogue of the classical Young integration [13]. As an application, we extend an argument of Schwartz [11] to rough differential equations, and prove the existence, uniqueness and continuity of the solution, which is applicable when the driving path takes values in nilpotent Lie group or Butcher group.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1681-1703.

Dates
First available in Project Euclid: 27 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1445951162

Digital Object Identifier
doi:10.2969/jmsj/06741681

Mathematical Reviews number (MathSciNet)
MR3417509

Zentralblatt MATH identifier
1345.60070

Subjects
Primary: 60H99: None of the above, but in this section
Secondary: 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03]

Keywords
rough paths theory Young integral integrable one-forms universal limit theorem

Citation

LYONS, Terry J.; YANG, Danyu. The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations. J. Math. Soc. Japan 67 (2015), no. 4, 1681--1703. doi:10.2969/jmsj/06741681. https://projecteuclid.org/euclid.jmsj/1445951162


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