Differential Equations driven by \Pi-rough paths

Author: 

Gyurko, L

Last Updated: 

2021-03-03T16:26:58.63+00:00

abstract: 

This paper revisits the concept of rough paths of inhomogeneous degree of smoothness (geometric \Pi-rough paths in our terminology) sketched by Lyons ("Differential equations driven by rough signals", Revista Mathematica Iber. Vol 14, Nr. 2,215-310, 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.

Symplectic id: 

354569

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article