Browsing by Author "Preiß, Rosa"

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    Mini-Workshop: Combinatorial and Algebraic Structures in Rough Analysis and Related Fields
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2023) Bruned, Yvain; Bellingeri, Carlo; Chevyrev, Ilya; Preiß, Rosa
    Recent years have seen an explosion of algebraic methods to study singular stochastic and rough dynamics. These include developments in geometric rough path theory based on the algebra of words, the introduction of decorated trees in regularity structures, and the recent approach to singular stochastic partial differential equations based on multi-indices. These developments have furthermore led to important links with numerical analysis, machine learning, stochastic quantisation, and the study of symmetries of physical systems. The aim of this mini-workshop was to bring together experts working on these fields using algebraic structures that appear in rough dynamics. The goal was to facilitate the exchange of ideas and encourage further connections to be established.
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    The moving frame method for iterated-integrals: Orthogonal invariants
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Diehl, Joscha; Preiß, Rosa; Ruddy, Michael; Tapia, Nikolas
    We explore the algebraic properties of a generalized version of the iterated-sums signature, inspired by previous work of F. Kiraly and H. Oberhauser. In particular, we show how to recover the character property of the associated linear map over the tensor algebra by considering a deformed quasi-shuffle product of words on the latter. We introduce three non-linear transformations on iterated-sums signatures, close in spirit to Machine Learning applications, and show some of their properties.