Related papers: Directed Chain Stochastic Differential Equations
In this article we study the convergence of a stochastic particle system that interacts through threshold hitting times towards a novel equation of McKean-Vlasov type. The particle system is motivated by an original model for the behavior…
We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes…
We consider interacting systems particle driven by i.i.d. fractional Brownian motions, subject to irregular, possibly distributional, pairwise interactions. We show propagation of chaos and mean field convergence to the law of the…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
We discuss the construction and approximation of solutions to a nonlinear McKean-Vlasov equation driven by a singular self-excitatory interaction of the mean-field type. Such an equation is intended to describe an infinite population of…
We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be non-linear and path…
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the limiting particle density is given by the unique solution of…
We study the local asymptotic normality (LAN) property for the likelihood function associated with discretely observed $d$-dimensional McKean-Vlasov stochastic differential equations over a fixed time interval. The model involves a joint…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
We study direct and inverse scattering problem for systems of interacting particles, having web-like structure. Such systems consist of a finite number of semi-infinite chains attached to the central part formed by a finite number of…
We consider a general McKean-Vlasov stochastic differential equation driven by a rotationally invariant $\alpha$-stable process on $\mathbb{R}^d$ with $\alpha \in (1,2)$. We assume that the diffusion coefficient is the identity matrix and…
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…
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 work, we prove the well-posedness and propagation of chaos for a stochastic particle system in mean-field interaction under the assumption that the interacting kernel belongs to a suitable $L_t^q-L_x^p$ space. Contrary to the large…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the…
McKean-Vlasov stochastic differential equations (MV-SDEs) provide a mathematical description of the behavior of an infinite number of interacting particles by imposing a dependence on the particle density. As such, we study the influence of…
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…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…