Differential Equations Driven by Π -Rough Paths
Lajos Gergely Gyurkó
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Source: Crossref
Published: Jan 21, 2016
DOI: 10.1017/s0013091515000474
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Abstract This paper revisits the concept of rough paths of inhomogeneous degree of smoothness (geometric Π -rough paths in our terminology) sketched by Lyons in 1998. Although geometric Π -rough paths can be treated as p -rough paths for a sufficiently large p , and the theory of integration of Lip γ one-forms ( γ > 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 Π -rough paths and give sufficient conditions for existence and uniqueness of solution.
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