Related papers: Propagation of chaos for doubly mean reflected BSD…
We consider backward stochastic differential equations (BSDEs) with mean-field and McKean-Vlasov interactions in their generators in a general setting, where the drivers are square-integrable martingales, with a focus on the independent…
Sequential propagation of chaos (SPoC) is a recently developed tool to solve mean-field stochastic differential equations and their related nonlinear Fokker-Planck equations. Based on the theory of SPoC, we present a new method (deepSPoC)…
In this paper, we study the backward stochastic differential equation (BSDE) with two nonlinear mean reflections, which means that the constraints are imposed on the distribution of the solution but not on its paths. Based on the backward…
In this article, we establish a propagation of chaos result for weakly interacting nonlinear Snell envelopes which converge to a class of mean-field reflected backward stochastic differential equations (BSDEs) with jumps and…
Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…
In this paper, we study a class of mean-field reflected backward stochastic differential equations (MF-RBSDEs) driven by a marked point process and also analyze MF-RBSDEs driven by a Poisson process. Based on a $g$-expectation…
In this paper, we deal with Reflected Backward Stochastic Differential Equations for which the constraint is not on the paths of the solution but on its law as introduced by Briand, Elie and Hu in [3]. We extend the recent work [2] of…
In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements.…
The purpose of the present paper is to introduce and establish a notion of stability for the backward propagation of chaos with respect to (initial) data sets. Consider, for example, a sequence of discrete-time martingales converging to a…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
As an enhanced version of existing results on Kac's propagation of chaos, which describes the convergence of mean-field particle systems to a system of independent McKean-Vlasov particles as the number of particles tends to infinity, we…
Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an…
This article is a continuation of our first work \cite{chaudruraynal:frikha}. We here establish some new quantitative estimates for propagation of chaos of non-linear stochastic differential equations in the sense of McKean-Vlasov. We…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
In contrast to ordinary stochastic differential equations (SDEs), the numerical simulation of McKean-Vlasov stochastic differential equations (MV-SDEs) requires approximating the distribution law first. Based on the theory of propagation of…
The paper studies a multi-dimensional mean-field reflected backward stochastic differential equation (MF-RBSDE) with a reflection constraint depending on both the value process $Y$ and its distribution $[Y]$. We establish the existence,…
We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: it has the same weak limit as…
This work addresses the propagation of chaos properties in a class of moderately interacting particle systems for the approximation of singular kinetic McKean-Vlasov SDEs driven by alpha-stable processes.
The present paper is devoted to the study of mean-field backward stochastic differential equations (MFBSDEs) with double mean reflections whose generators are not Lipschitz continuous. With the help of the Skorokhod problem and some a…