Propriétés fines des trajectoires du mouvement brownien fractionnaire

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We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

The probability of detecting technosignatures (i.e., evidence of technological activity beyond Earth) increases with their longevity, or the time interval over which they manifest. Therefore, the assumed distribution of longevities has some bearing on the ...

We establish a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterm ...

One major challenge in distributed learning is to efficiently learn for each client when the data across clients is heterogeneous or non iid (not independent or identically distributed). This provides a significant challenge as the data of the other client ...

Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

We study the existence and propagation of singularities of the solution to a one-dimensional linear stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. Our approach is based on a simultaneous law of the ...

In a groundbreaking work, Duplantier, Miller and Sheffield showed that subcritical Liouville quantum gravity (LQG) coupled with Schramm-Loewner evolutions (SLE) can be obtained by gluing together a pair of Brownian motions. In this paper, we study the coun ...

We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions. We also establish a Chung-type law of the iterated logarithm. The results ...

Peaks-over-threshold analysis using the generalised Pareto distribution is widely applied in modelling tails of univariate random variables, but much information may be lost when complex extreme events are studied using univariate results. In this paper, w ...

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate an ...

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogenei ...

The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, ...

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an under-damped form of the Langevin algorithm perfor ...

We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for n-sided dice with pairwise ordering induced by the probability, relative to 1/2, that a throw from one die is higher than the other. We ...

Propriétés fines des trajectoires du mouvement brownien fractionnaire

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Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Additive and geometric transversality of fractal sets in the integers

Technosignatures Longevity and Lindy's Law

Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields

Personalized Privacy-Preserving Distributed Learning on Heterogeneous Data

Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solution

Stochastic particle transport by deep-water irregular breaking waves

Preconditioners for robust optimal control problems under uncertainty

Propagation of singularities for the stochastic wave equation

Brownian half-plane excursion and critical Liouville quantum gravity

The Hausdorff measure of the range and level sets of Gaussian random fields with sectorial local nondeterminism

Functional peaks-over-threshold analysis

Stable high-order randomized cubature formulae in arbitrary dimension

A Functional Perspective on Information Measures

On Linear Optimization over Wasserstein Balls

Relative, local and global dimension in complex networks

Scenario Reduction Revisited: Fundamental Limits and Guarantees

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Is there an analog of Nesterov acceleration for gradient-based MCMC?

The probability of intransitivity in dice and close elections