15 citations · 46 across the 9 of their papers we have counts for
9 papers
Approximate Transitivity of Young Translation on Rough Paths
Carlo Bellingeri, Paul Gassiat, Hugo Nouaille
We show that Young translation has dense orbits in the space of rough paths: for any two geometric rough paths, one can translate the first by a sequence of smooth paths so that it…
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…
Generalized Euler-Maclaurin formula and Signatures
Carlo Bellingeri, Peter K. Friz, Sylvie Paycha
The Euler-Maclaurin formula which relates a discrete sum with an integral, is generalised to the setting of Riemann-Stieltjes sums and integrals on stochastic processes whose paths…
Branched Itô formula and natural Itô-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 , constitute integration theories that may fai…
Smooth rough paths, their geometry and algebraic renormalization
Carlo Bellingeri, Peter K. Friz, Sylvie Paycha +1
We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometr…
Quasi-geometric rough paths and rough change of variable formula
Carlo Bellingeri
Using some basic notions from the theory of Hopf algebras and quasi-shuffle algebras, we introduce rigorously a new family of rough paths: the quasi-geometric rough paths. We discu…
Singular paths spaces and applications
Carlo Bellingeri, Peter K. Friz, Máté Gerencsér
Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related object…
Transport and continuity equations with (very) rough noise
Carlo Bellingeri, Ana Djurdjevac, Peter K. Friz +1
Existence and uniqueness for rough flows, transport and continuity equations driven by general geometric rough paths are established.
An Itô type formula for the additive stochastic heat equation
Carlo Bellingeri
We use the theory of regularity structures to develop an Itô formula for , the solution of the one dimensional stochastic heat equation driven by space-time white noise with per…