arXiv subjects

Mohammed Elhachemy

Publications and source records attributed to Mohammed Elhachemy.

2 recordsLinked to original sources

arXiv2026

On a class of Reflected Mean-Field Stochastic Differential Equations with jumps

This paper investigates a class of Reflected Mean-Field Stochastic Differential Equations when the noise is driven by a Brownian motion and an independent Poisson measure. We prove the existence and uniqueness of solutions and provide moments estimates for the state processes. We apply our result to derive a Feynman-Kac formula for the solution of an Integral-Partial Differential Equation with Neumann boundary conditions.

math.PR↗

arXiv2026

Reflected generalized BDSDEs driven by non-homogeneous Lévy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions

We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous Lévy process. Under stochastic conditions on the coefficients, we prove the existence and uniqueness of a solution. Furthermore, we apply these results to obtain a probabilistic representation for the viscosity solutions of an obstacle problem governed by stochastic integro-partial differential equations with a nonlinear Neumann boundary condition.

math.PR↗