arXiv subjects
Publications and source records attributed to Nikolas Tapia.
Signatures provide a succinct description of certain features of paths in a reparametrization invariant way. We propose a method for classifying shapes based on signatures, and compare it to current approaches based on the SRV transform and dynamic programming.
We present an approach to classical definitions and results on cumulant--moment relations and Wick polynomials based on extensive use of convolution products of linear functionals on a coalgebra. This allows, in particular, to understand the construction of Wick polynomials as the result of a Hopf algebra deformation under the action of linear automorphisms induced by multivariate moments associated to an arbitrary family of random variables with moments of all orders. We also generalise the notion of deformed product in order to discuss how these ideas appear in the recent theory of regularity structures.