Related papers: Mean Field Stochastic Partial Differential Equatio…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
We study invariant random fields of nonlinear multiplicative stochastic heat equations in the weak disorder regime. Under a natural second-moment condition, we show that positive invariant fields are in one-to-one correspondence with…
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…
In this paper we consider stochastic Fokker-Planck Partial Differential Equations (PDEs), obtained as the mean-field limit of weakly interacting particle systems subjected to both independent (or idiosyncratic) and common Brownian noises.…
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…
We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in ${\mathbb R}^3$. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to $\frac1N$ where $N$…
We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem,…
We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounded coefficients with possibly unbounded diffusion…
Statistical systems composed of atoms interacting with each other trough nonintegrable interaction potentials are considered. Examples of these potentials are hard-core potentials and long-range potentials, for instance, the Lennard-Jones…
We introduce two algorithms based on a policy iteration method to numerically solve time-dependent Mean Field Game systems of partial differential equations with non-separable Hamiltonians. We prove the convergence of such algorithms in…
The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…
We study the problem of reconstructing interaction kernels in systems of interacting agents from macroscopic measurements when posed as an optimization problem. The reconstruction procedure depends on the formulation of the forward model,…
The purpose of this article is to derive the crossover from the Ornstein-Uhlenbeck process to energy solutions of the stochastic Burgers equation with characteristic operators given in terms of fractional operators, such as the regional…
Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…
Covariant stochastic partial differential equations are studied in any dimension. A special class of such equations is selected and it is proven that the solutions can be analytically continued to Minkowski space-time yielding tempered…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…
In this paper we consider a variational problem related to a model for a nucleon interacting with the $\omega$ and $\sigma$ mesons in the atomic nucleus. The model is relativistic, and we study it in a nuclear physics nonrelativistic limit,…
We report on a simple strategy to treat mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. Extending the method of counting, introduced in [Lett. Math.…