6 papers · 1 filter
Affine Structure of the Brownian Signature
Eduardo Abi Jaber, Elie Attal, Dimitri Sotnikov
We establish an infinite-dimensional affine transform theory for the time-augmented Brownian signature. Our first main result shows that, for a suitable class of linear functions o…
Volterra clocks and their pure-jump limits: hitting times of curved boundaries
Eduardo Abi Jaber, Elie Attal, Andreas Sojmark
We introduce a class of continuous Volterra processes, called Volterra clocks, and study their singular limit as the memory kernel collapses to a Dirac mass at zero. The dynamics a…
Efficient Simulation of Hawkes Processes using their Affine Volterra Structure
Eduardo Abi Jaber, Elie Attal, Dimitri Sotnikov
We introduce a novel and efficient simulation scheme for Hawkes processes on a fixed time grid, leveraging their affine Volterra structure. The key idea is to first simulate the in…
From Hyper Roughness to Jumps as
Eduardo Abi Jaber, Elie Attal, Mathieu Rosenbaum
We investigate the weak limit of the hyper-rough square-root process as the Hurst index goes to . This limit corresponds to the fractional kernel losing…
Eigenvector Overlaps of Random Covariance Matrices and their Submatrices
Elie Attal, Romain Allez
We consider the singular vectors of any submatrix of a rectangular Gaussian matrix and study their asymptotic overlaps with those of the full matrix, in t…
Interlacing Eigenvectors of Large Gaussian Matrices
Elie Attal, Romain Allez
We consider the eigenvectors of the principal minor of dimension of the Dyson Brownian motion in and investigate their asymptotic overlaps with the eigenvec…