Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 67, Number 4 (2015), 1681-1703.
The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations
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 . As an application, we extend an argument of Schwartz  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.
J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1681-1703.
First available in Project Euclid: 27 October 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H99: None of the above, but in this section
Secondary: 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03]
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