Related papers: Mean-Field Control for Diffusion Aggregation syste…
In this paper, the well-posedness of two-dimensional signal-dependent Keller-Segel system and its mean-field derivation from a interacting particle system on the whole space are investigated. The signal dependence effect is reflected by the…
In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…
This paper continues our survey about the mean-field derivation of the two-dimensional signal-dependent Keller-Segel system studied in [1]. Therefore, we consider the same system of moderately interacting particles as before. The difference…
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems. To solve proposed optimal control problems numerically, we…
We study the convergence problem of mean-field control theory in the presence of state constraints and non-degenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems…
We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state…
We rigorously derive a two-dimensional Keller-Segel type system with signal-dependent sensitivity from a stochastic interacting particle model. By employing suitably defined stopping times, we prove that the convergence of the interacting…
The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations.…
A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…
We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary…
In this work, we prove the well--posedness of a singularly interacting stochastic particle system and we establish propagation of chaos result towards the one-dimensional parabolic-parabolic Keller-Segel model.
In this paper, we study propagation of chaos for the parabolic-parabolic Keller-Segel model with a logarithmic cut-off by establishing a rigorous convergence analysis from a stochastic particle system to the parabolic-parabolic Keller-Segel…
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise…
A parabolic-parabolic (Patlak-) Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy…
In this work, we study the mean field Schr\"odinger problem from a purely probabilistic point of view by exploiting its connection to stochastic control theory for McKean-Vlasov diffusions. Our main result shows that the mean field…
This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of…
This work is a series of two articles. The main goal is to rigorously derive the degenerate parabolic-elliptic Keller-Segel system in the sub-critical regime from a moderately interacting stochastic particle system. In the first article…
This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…
In the present work, we develop a novel particle method for a general class of mean field control problems, with source and terminal constraints. Specific examples of the problems we consider include the dynamic formulation of the…