Related papers: Control Problem on Space of Random Variables and M…
The stochastic optimal control of many agents is an important problem in various fields. We investigate the problem of partial observations, where the state of each agent is not fully observed and the control must be decided based on noisy…
We consider the stochastic Landau-Lifshitz-Gilbert equation in dimension 1. A control process is added to the effective field. We show the existence of a weak martingale solution for the resulting controlled equation. The proof uses the…
This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…
This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional…
This paper mainly establishes the finite-horizon stochastic bounded real lemma, and then solves the $H_{\infty}$ control problem for discrete-time stochastic linear systems defined on the separable Hilbert spaces, thereby unifying the…
In this article, by using several new crucial {\it a priori} estimates which are still absent in the literature, we provide a comprehensive resolution of the first order generic mean field type control problems and also establish the…
In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…
In the first part of this paper, we derive an infinite dimensional partial differential equation which describes an economic equilibrium in a model of storage which includes an infinite number of non-atomic agents. This equation has the…
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
This paper is devoted to the study of the eigenvalues of the Wishart process which are the analogof the Dyson Brownian Motion for covariance matrices. Such processes were in particular studied byBru. The mean field convergence of the…
This paper contains a study of multivariate second order stochastic mappings indexed by an abstract set $\Lambda$ in close connection to their operator covariance functions. The characterizations of the normal Hilbert module or of Hilbert…
We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of…
A new formalism to express and operate on diversity measures of qualitative variables, built in a Hilbert space, is presented. The abstract character of the Hilbert space naturally incorporates the equivalence between qualitative variables…
In the last few years there has been renewed interest in the classical control problem of de Finetti for the case that underlying source of randomness is a spectrally negative Levy process. In particular a significant step forward is made…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
In this article, we provide a numerical method based on fitted finite volume method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from stochastic optimal control problems. The computational challenge is due to the nature…
Optimal control of interacting particles governed by stochastic evolution equations in Hilbert spaces is an open area of research. Such systems naturally arise in formulations where each particle is modeled by stochastic partial…
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…
The results in the paper are related to the classification problem for invariant subspaces of multiplication operators in several variables. The main results consist of characterizations, in the two dimensional case, of ideals of…