arXiv subjects

Foivos Katsetsiadis

Publications and source records attributed to Foivos Katsetsiadis.

3 recordsLinked to original sources

arXiv2024

Geometric embedding for regularity structures

In this paper, we show how one can view certain models in regularity structures as some form of geometric rough paths. This is performed by identifying the deformed Butcher-Connes-Kreimer Hopf algebra with a quotient of the shuffle Hopf algebra which is the structure underlying the definition of a geometric rough path. This provides an extension of the isomorphism between the Butcher-Connes-Kreimer Hopf algebra and the shuffle Hopf algebra. This new algebraic result relies strongly on the deformation formalism and the post-Lie structures introduced recently in the context of regularity structures.

math.PR↗

arXiv2023

Post-Lie algebras in Regularity Structures

In this work, we construct the deformed Butcher-Connes-Kreimer Hopf algebra coming from the theory of Regularity Structures as the universal envelope of a post-Lie algebra. We show that this can be done using either of the two combinatorial structures that have been proposed in the context of singular SPDEs: decorated trees and multi-indices. Our construction is inspired from multi-indices where the Hopf algebra was obtained as the universal envelope of a Lie algebra and it has been proved that one can find a basis that is symmetric with respect to certain elements. We show that this Lie algebra comes from an underlying post-Lie structure.

math.PR↗

arXiv2022

Ramification of Volterra-type Rough Paths

We extend the new approach introduced in arXiv:1912.02064v2 [math.PR] and arXiv:2102.10119v1 [math.PR] for dealing with stochastic Volterra equations using the ideas of Rough Path theory and prove global existence and uniqueness results. The main idea of this approach is simple: Instead of the iterated integrals of a path comprising the data necessary to solve any equation driven by that path, now iterated integral convolutions with the Volterra kernel comprise said data. This leads to the corresponding abstract objects called Volterra-type Rough Paths, as well as the notion of the convolution product, an extension of the natural tensor product used in Rough Path Theory.

math.PR↗