From the 1 of 7 linked papers with an AI index.
7 papers
Concise -representations of a path
Emilio Ferrucci, Oliver Perrée, Terry Lyons
The paper investigates how to store a path using a truncated log-signature with the optimal balance between the number of intervals and signature degree, minimizing memory while gu…
Locality of rough path lifts
Ilya Chevyrev, Emilio Ferrucci
Every Hölder continuous path admits a geometric rough path lift by the Lyons--Victoir extension theorem. A natural question that emerges when lifting more than…
Rough differential equations for volatility
Ofelia Bonesini, Emilio Ferrucci, Ioannis Gasteratos +1
We introduce a canonical way of performing the joint lift of a Brownian motion and a low-regularity adapted stochastic rough path , extending [Diehl, Oberhauser and…
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…
Wick integrals
Carlo Bellingeri, Emilio Ferrucci
We introduce the Wick integral for a class of stochastic processes of bounded -variation which are not necessarily Gaussian. Th…
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.…