scholarly journals Differential equations driven by rough paths with jumps

2018 ◽  
Vol 264 (10) ◽  
pp. 6226-6301 ◽  
Author(s):  
Peter K. Friz ◽  
Huilin Zhang
Keyword(s):  
Differential Equations ◽  
Rough Paths

Differential Equations Driven by Rough Paths

2007 ◽  
Author(s):  
Terry J. Lyons ◽  
Michael Caruana ◽  
Thierry Lévy
Keyword(s):  
Differential Equations ◽  
Rough Paths

scholarly journals Planarly branched rough paths and rough differential equations on homogeneous spaces

2020 ◽  
Vol 269 (11) ◽  
pp. 9740-9782
Author(s):  
C. Curry ◽  
K. Ebrahimi-Fard ◽  
D. Manchon ◽  
H.Z. Munthe-Kaas
Keyword(s):  
Differential Equations ◽  
Homogeneous Spaces ◽  
Rough Paths

Differential Equations Driven byΠ-Rough Paths

2016 ◽  
Vol 59 (3) ◽  
pp. 741-758 ◽  
Author(s):  
Lajos Gergely Gyurkó
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Uniqueness Of Solution ◽  
Rough Paths ◽  
Weaker Conditions

AbstractThis paper revisits the concept of rough paths of inhomogeneous degree of smoothness (geometricΠ-rough paths in our terminology) sketched by Lyons in 1998. Although geometricΠ-rough paths can be treated asp-rough paths for a sufficiently largep, and the theory of integration of Lipγone-forms (γ>p–1) along geometricp-rough paths applies, we prove the existence of integrals of one-forms under weaker conditions. Moreover, we consider differential equations driven by geometricΠ-rough paths and give sufficient conditions for existence and uniqueness of solution.

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