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19942026
most citedTraining Schrödinger's cat: quantum optimal control

779 citations

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math.PR2025

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…

math.PR2025

Functional Limit Theorems for the range of stable random walks

Maxence Baccara

In this paper we establish Functional Limit Theorems for the range of random walks in that are in the domain of attraction of a non-degenerate -stable process in…

math.PR2025

Long time behavior and Yaglom limit for real trait-structured Birth and Death Processes

Pierre Collet, Sylvie Méléard, Jaime San

In this article we study the long time behaviour of measure-valued birth and death processes in continuous time, where the dynamics between jumps are one-dimensional Markov process…

math.PR2025

Exponentially Fading Memory Signature

Eduardo Abi Jaber, Dimitri Sotnikov

We introduce the exponentially fading memory (EFM) signature, a time-invariant transformation of an infinite (possibly rough) path that serves as a mean-reverting analogue of the c…

math.PR2025

Weak solutions of Stochastic Volterra Equations in convex domains with general kernels

Eduardo Abi Jaber, Aurélien Alfonsi, Guillaume Szulda

We establish new weak existence results for -dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution…

math.PR2025

Stochastic numerical approximation for nonlinear Fokker-Planck equations with singular kernels

Nicoleta Cazacu

This paper studies the convergence rate of the Euler-Maruyama scheme for systems of interacting particles used to approximate solutions of nonlinear Fokker-Planck equations with si…