Related papers: Martingale approximations for random fields

We obtain an almost sure limit theorem for the maximum of nonstationary random fields under some dependence conditions.

Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…

This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as…

We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obtaining these point evaluations is costly, minimising the…

Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such…

We propose an efficient solution approach for high-dimensional nonlocal mean-field game (MFG) systems based on the Monte Carlo approximation of interaction kernels via random features. We avoid costly space-discretizations of interaction…

We prove that on an atomless probability space, the worst-case mean squared error of the Monte-Carlo estimator is minimal if the random points are chosen independently.

This article studies optional and predictable projections of integrands and convex-valued stochastic processes. The existence and uniqueness are shown under general conditions that are analogous to those for conditional expectations of…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

We present several Ito-Wentzell formulae on Wiener spaces for real-valued functional random field of Ito type that depend on measure flows. We distinguish the full- and the marginal-measure flow cases in the spirit of mean-field games.…

Gaussian random field is a ubiquitous model for spatial phenomena in diverse scientific disciplines. Its approximation is often crucial for computational feasibility in simulation, inference, and uncertainty quantification. The…

We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…

The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…

We extend the notion of the associated random walk and the Wald martingale in random walks where the increments are independent and identically distributed to the more general case of stationary ergodic increments. Examples are given where…

In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…

This paper provides sufficient conditions over the sequence of samples and parameters of an adaptive Markov Chain Monte Carlo (MCMC) algorithm to ensure ergodicity with respect to a target distribution that can have unbounded support. These…

We are presenting a method of linear regression based on Gram-Schmidt orthogonal projection that does not compute a pseudo-inverse matrix. This is useful when we want to make several regressions with random data vectors for simulation…

The Random Orthogonal Model (ROM) of Marinari-Parisi-Ritort [MPR1,MPR2] is a model of statistical mechanics where the couplings among the spins are defined by a matrix chosen randomly within the orthogonal ensemble. It reproduces the most…

We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…

Often we wish to predict a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling, combining the…