Related papers: Martingale approximations for random fields

Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…

We consider a multivariate piecewise linear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured by the integrated mean square error. Multivariate piecewise linear interpolator is…

We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…

We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…

Herein, we introduce and study a new class of discrete random fields designed for quick simulation and covariance inference under inhomogeneous condition. Simulation of these correlated fields can be done in a single pass instead of relying…

We generalise the martingale-coboundary representation of discrete time stochastic processes to the non-stationary case and to random variables in Orlicz spaces. Related limit theorems (CLT, invariance principle, log log law, probabilities…

We introduce a class of Markov chains, that contains the model of stochastic approximation by averaging and non-averaging. Using martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions…

For the Narain-Horvitz-Thompson estimator to have usual asymptotic properties such as consistency, some conditions on the sampling design and on the variable of interest are needed. Cardot et al. (2010) give some sufficient conditions for…

Mean-field approximation is often used to explore the qualitative behaviour of phase transitions in classical spin models before employing computationally costly methods such as the Monte-Carlo techniques. We implement a 'lattice…

In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…

We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the…

The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…

We establish general conditions under which there exists uniform in time convergence between a stochastic process and its approximated system. These standardised conditions consist of a local in time estimate between the original and the…

We establish a quantitative normal approximation result for sums of random variables with multilevel local dependencies. As a corollary, we obtain a quantitative normal approximation result for linear functionals of random fields which may…

A randomised trapezoidal quadrature rule is proposed for continuous functions which enjoys less regularity than commonly required. Indeed, we consider functions in some fractional Sobolev space. Various error bounds for this randomised rule…

We investigate the nonparametric estimation for regression in a fixed-design setting when the errors are given by a field of dependent random variables. Sufficient conditions for kernel estimators to converge uniformly are obtained. These…

Mean field approximation is a popular method to study the behaviour of stochastic models composed of a large number of interacting objects. When the objects are asynchronous, the mean field approximation of a population model can be…

We show that the existence of a martingale approximation of a stationary process depends on the choice of the filtration. There exists a stationary linear process which has a martingale approximation with respect to the natural filtration,…

For a class of symmetric random matrices whose entries are martingale differences adapted to an increasing filtration, we prove that under a Lindeberg-like condition, the empirical spectral distribution behaves asymptotically similarly to a…

In this paper, we present finite element approximations of a class of Generalized random fields defined over a bounded domain of R d or a smooth d-dimensional Riemannian manifold (d $\ge$ 1). An explicit expression for the covariance matrix…