5 papers · 1 filter
Random dynamical systems generated by rough differential equations driven by controlled rough paths
Xing Gao, Jiaqi Liu
We study rough differential equations driven by controlled rough paths with drift. By means of the canonical lift of the controlled driver, we establish pathwise well-posedness and…
The planar Hopf algebra of noncommutative multi-indices
Yong Yu, Xing Gao, Dominique Manchon
We construct the planar Linares--Otto--Tempelmayr Hopf algebra, thereby filling the missing planar noncommutative multi-index corner in the square relating the LOT, Butcher--Connes…
Exact Signature Tail Asymptotics for Pure Rough Paths
Nannan Li, Xing Gao
We prove~\cite[Conjecture 2.12]{BGS20} on the signature tail asymptotics of pure rough paths and extend it to arbitrary reasonable tensor norms. In more details, let \[ \mathbf X_t…
A Low-Regularity Semigroup Sewing Lemma via Quotient Structures
Nannan Li, Xing Gao
We develop a low-regularity Sewing theory for the semigroup coboundary associated with a strongly continuous semigroup . Unlike the ordinary low-regularity Sewing pr…
Jump Itô-type formula with arbitrary regularity
Nannan Li, Xing Gao
We establish an Itô-type formula for finite -variation paths with jumps for arbitrary . The formula is stated in a fully pathwise form and separates the reduced rough i…