arXiv subjects

Imane Jarni

Publications and source records attributed to Imane Jarni.

5 recordsLinked to original sources

arXiv2025

Multidimensional McKean-Vlasov SDEs with mean reflection: well-posedness and existence of optimal control

In this work, we investigate the multidimensional Skorokhod problem for c\`adl\`ag processes, where the reflection is subject to a minimality condition depending on the law of the solution. We then apply these results to establish existence and uniqueness for multidimensional McKean-Vlasov stochastic differential equations with mean reflection. Finally, we address the existence of optimal relaxed controls for such equations.

math.PR↗

arXiv2025

Mean Field Games with Reflected Dynamics

This paper establishes an equilibrium existence result for a class of Mean Field Games involving Reflected Stochastic Differential Equations. The proof relies on the framework of relaxed controls and martingale problems.

math.PR↗

arXiv2024

Reflected Mckean-Vlasov stochastic differential equations with jumps in time-dependent domains

In this paper, we investigate the deterministic multidimensional Skorokhod problem with normal reflection in a family of time-dependent convex domains that are càdlàg with respect to the Hausdorff metric. We then show the existence and uniqueness of solutions to multidimensional McKean-Vlasov stochastic differential equations reflected in these time-dependent domains. Additionally, we derive stability properties with respect to the initial condition and the coefficients. Finally, we establish a propagation of chaos result.

math.PR↗

arXiv2022

Stochastic differential equations with respect to optional semimartingales and two reflecting regulated barriers

In this work, we introduce a new Skorokhod problem with two reflecting barriers when the trajectories of the driven process and the barriers are right and left limited. We show that this problem has an explicit unique solution in a deterministic case. Then, we apply our result to study the existence and uniqueness of solutions of reflected stochastic differential equations with respect to optional semimartingales. The study is carried out on a probability space that does not necessarily satisfy the usual conditions.

math.PR↗

arXiv2019

On Skorokhod Problem with Two RCLL Reflecting Completely Separated Barriers

In this paper we deal with Skorokhod problem for right continuous left limited (rcll) barriers. We prove existence and uniqueness of the solution when the barriers are only supposed to be rcll and completely separated. Then, we apply our results to prove existence and uniqueness of the solution of a reflected stochastic differential equation (SDE).

math.PR↗