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math.PR2026
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…
math.PR2026
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…