Emilio Ferrucci

works on

controlled differential equations 1 log-signature 1 numerical approximation 1 path signatures 1 rough paths 1 stochastic differential equations 1

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math.PR2026

Locality of rough path lifts

Ilya Chevyrev, Emilio Ferrucci

Every Hölder continuous path $X$ admits a geometric rough path lift $X$ by the Lyons--Victoir extension theorem. A natural question that emerges when lifting more than…

math.PR2026

Orthogonal polynomials on path-space

Ilya Chevyrev, Emilio Ferrucci, Darrick Lee +3

We consider the orthogonalisation of the signature of a stochastic process as the analogue of orthogonal polynomials on path-space. Under an infinite radius of convergence assumpti…

math.PR2025

Wick integrals

Carlo Bellingeri, Emilio Ferrucci

We introduce the Wick integral $\int_{s}^{t} f (X_{u}) ◊ d X_{u}$ for a class of stochastic processes $X$ of bounded $2 > p$ -variation which are not necessarily Gaussian. Th…

math.PR2025

High-degree cubature on Wiener space through unshuffle expansions

Emilio Ferrucci, Timothy Herschell, Christian Litterer +1

Utilising classical results on the structure of Hopf algebras, we develop a novel approach for the construction of cubature formulae on Wiener space based on unshuffle expansions.…

math.PR2025

Branched ItÃ´ formula and natural ItÃ´-Stratonovich isomorphism

Carlo Bellingeri, Emilio Ferrucci, Nikolas Tapia

Branched rough paths, defined as paths with values in the character group of the Connes-Kreimer Hopf algebra $H_{CK}$ , constitute integration theories that may fai…