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math.PR2026
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…
math.PR2026
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…
math.PR2026
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…
math.PR2026
Universal limit theorem for rough differential equations driven by controlled rough paths
Nannan Li, Xing Gao
We study rough differential equations driven by controlled rough paths in the level- regime . Given a reference rough path and an $\mat…