Related papers: Sticky nonlinear SDEs and convergence of McKean-Vl…
This paper focuses on the invariant measure of McKean-Vlasov (MV) stochastic differential equations (SDEs) with common noise (wCN) whose coefficients depend on both the state and the measure. Using the existence of the unique solution of…
Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
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.…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
This paper studies McKean-Vlasov stochastic differential equations (MVSDEs) whose drift coefficients grow super-linearly in both state variables and measure arguments, and whose diffusion coefficients exhibit super-linear growth in the…
Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…
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 paper studies the numerical methods to approximate the solutions for a sort of McKean-Vlasov neutral stochastic differential delay equations (MV-NSDDEs) that the growth of the drift coefficients is super-linear. First, We obtain that…
We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump L\'{e}vy processes. We prove a uniform in time propagation of chaos result, providing quantitative bounds on…
In this article, we consider McKean stochastic differential equations, as well as their corresponding McKean-Vlasov partial differential equations, which admit a unique stationary state, and we study the linearized It\^o diffusion process…
This paper focus on investigating the explicit rate of convergence for the propagation of chaos, in a pathwise sense a family of interacting stochastic particle related to some Brownian driven McKean-Vlasov dynamics. Precisely the McKean…
We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…
We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field…
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…
In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…
We prove the well-posedness of solutions to McKean-Vlasov stochastic differential equations driven by L\'evy noise under mild assumptions where, in particular, the L\'evy measure is not required to be finite. The drift, diffusion and jump…
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…
In this note, under a weak monotonicity and a weak coercivity, we address strong well-posedness of McKean-Vlasov stochastic differential equations (SDEs) driven by L\'{e}vy jump processes, where the coefficients are Lipschitz continuous…
The couplings by change of measure are applied to establish log-Harnack inequality(equivalently the entropy-cost estimate) for conditional McKean-Vlasov SDEs and derive the quantitative conditional propagation of chaos in relative entropy…