Publications associées à Loi des grands nombres

Technosignatures Longevity and Lindy's Law

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 ...

Iop Publishing Ltd2024

Detecting whether a stochastic process is finitely expressed in a basis

Victor Panaretos, Neda Mohammadi Jouzdani

Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Peak Value-at-Risk Estimation for Stochastic Differential Equations using Occupation Measures

Matteo Raphael Tacchi

This paper proposes an algorithm to upper-bound maximal quantile statistics of a state function over the course of a Stochastic Differential Equation (SDE) system execution. This chance-peak problem is posed as a nonconvex program aiming to maximize the Va ...

IEEE2023

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

Victor Panaretos, Neda Mohammadi Jouzdani

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 ...

Elsevier2024

Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs

Robert Dalang, Carsten Hao Ye Chong

We consider a class of parabolic stochastic PDEs on bounded domains D c Rd that includes the stochastic heat equation but with a fractional power gamma of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces ...

INT STATISTICAL INST2023

A continuum approximation approach to the depot location problem in a crowd-shipping system

Nikolaos Geroliminis, Patrick Stefan Adriaan Stokkink

Last-mile delivery in the logistics chain contributes to congestion in urban networks due to frequent stops. Crowd-shipping is a sustainable and low-cost alternative to traditional delivery but relies heavily on the availability of occasional couriers. In ...

PERGAMON-ELSEVIER SCIENCE LTD2023

The exploration process of critical Boltzmann planar maps decorated by a triangular O(n) loop model

Aleksandra Korzhenkova

In this paper we investigate pointed (q, g, n)-Boltzmann loop-decorated maps with loops traversing only inner triangular faces. Using peeling exploration Budd (2018) modified to this setting we show that its law in the non-generic critical phase can be cod ...

IMPA2022

Testing For The Rank Of A Covariance Operator

Victor Panaretos

How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional dat ...

INST MATHEMATICAL STATISTICS-IMS2022

Simulating energetic particle losses in JET plasmas with a reverse integration biasing scheme

Mario Ludovico Podesta, Matteo Vallar

An integrated energetic particle transport model has been constructed in JET plasmas constrained by experimental fast ion loss measurements. The model incorporates a synthetic fast ion loss detector identical to JET's thin-foil Faraday cup fast ion loss de ...

IOP Publishing Ltd2022

Comparison of particle number size distribution trends in ground measurements and climate models

Jakob Boyd Pernov

Despite a large number of studies, out of all drivers of radiative forcing, the effect of aerosols has the largest uncertainty in global climate model radiative forcing estimates. There have been studies of aerosol optical properties in climate models, but ...

Copernicus Publications2022