Related papers: Eigenfunction martingale estimators for interactin…
This article studies the finite sample behaviour of a number of estimators for the integrated power volatility process of a Brownian semistationary process in the non semi-martingale setting. We establish three consistent feasible…
This paper provides unified calculations regarding certain measures and transformations in interacting particle systems. More specifically, we provide certain general conditions under which an interacting particle system will have a…
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for…
We present a Mean Field Game approach to obtain the rate function for the empirical measure of interacting particles under McKean-Vlasov dynamics. Although the result is well known, our approach relies on PDE methods and provides another…
We investigate the quench dynamics of the transverse field Ising model on a finite fully connected lattice as a prime example of non-equilibrium mean field dynamics. Using a rate function approach we compute the leading order corrections to…
An inversion method is formulated for extracting entanglement-related information on two-particle interactions in a one-dimensional system from measurable one-particle position- and momentum-distribution functions. The method is based on a…
This work focuses on the mean field stochastic partial differential equations with nonlinear kernels. We first prove the existence and uniqueness of strong and weak solutions for mean field stochastic partial differential equations in the…
In this paper, we define a quantum analogue of the notion of empirical measure in the classical mechanics of $N$-particle systems. We establish an equation governing the evolution of our quantum analogue of the $N$-particle empirical…
Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…
We propose a method to efficiently estimate the Laplacian eigenvalues of an arbitrary, unknown network of interacting dynamical agents. The inputs to our estimation algorithm are measurements about the evolution of a collection of agents…
We study recursive maximum likelihood estimation for stochastic interacting particle systems based on continuous observation of a single particle. In this regime, consistent estimation of the finite-particle log-likelihood is not possible,…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
We investigate reinforcement learning in the setting of Markov decision processes for a large number of exchangeable agents interacting in a mean field manner. Applications include, for example, the control of a large number of robots…
We consider a finite number of $N$ statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on…
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
A general theory of efficient estimation for ergodic diffusion processes sampled at high frequency with an infinite time horizon is presented. High frequency sampling is common in many applications, with finance as a prominent example. The…
We report a simple, efficient manner to assess magnetic interactions, more specifically the exchange interaction, in systems as blocked magnetic nanoparticles. Specifically, we investigate what is the theoretical limit for the external…
We show how the infinitesimal exchangeable pairs approach to Stein's method combines naturally with the theory of Markov semigroups. We present a multivariate normal approximation theorem for functions of a random variable invariant with…
We consider a system of $N$ particles interacting through their empirical distribution on a finite state space in continuous time. In the formal limit as $N\to\infty$, the system takes the form of a nonlinear (McKean--Vlasov) Markov chain.…