English
Related papers

Related papers: Rescaled Lotka-Volterra Models Converge to Super S…

200 papers

Loosely speaking, the Navier-Stokes-$\alpha$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $\alpha$. Starting from a strong two-dimensional solution to the Navier-Stokes-$\alpha$ model…

Analysis of PDEs · Mathematics 2022-10-06 Jad Doghman , Ludovic Goudenège

The recent contribution Dieker & Mikosch (2015) [1] obtained important representations of max-stable stationary Brown-Resnick random fields $\zeta_Z$ with a spectral representation determined by a Gaussian process $Z$. With motivations from…

Probability · Mathematics 2017-06-13 Enkelejd Hashorva

The results presented in this paper are a natural development of those described in the paper {\it The Volterra Integrable case. Novel analytical and numerical results} (OCNMP Vol.4 (2024) pp 188-211), where the authors reconsidered the…

Exactly Solvable and Integrable Systems · Physics 2025-06-11 Orlando Ragnisco , Federico Zullo

Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…

Probability · Mathematics 2013-02-19 Clément Dombry , Paul Jung

The goal of this paper is to prove rigorous results for the behavior of genealogies in a one-dimensional long range biased voter model introduced by Hallatschek and Nelson [25]. The first step, which is easily accomplished using results of…

Probability · Mathematics 2021-01-12 Rick Durrett , Wai-Tong Louis Fan

By means of white noise analysis, we prove some limit theorems for nonlinear functionals of a given Volterra process. In particular, our results apply to fractional Brownian motion (fBm) and should be compared with the classical convergence…

Probability · Mathematics 2010-11-30 Sébastien Darses , Ivan Nourdin , David Nualart

We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the…

Statistics Theory · Mathematics 2025-05-14 Pablo Ramses Alonso-Martin , Horatio Boedihardjo , Anastasia Papavasiliou

A Vitali-type theorem for vector lattice-valued modulars with respect to filter convergence is proved. Some applications are given to modular convergence theorems for moment operatorsin the vector lattice setting, and also for the Brownian…

Functional Analysis · Mathematics 2015-07-24 Antonio Boccuto , Domenico Candeloro , Anna Rita Sambucini

Statistical modelling of spatial extreme events has gained increasing attention over the last few decades with max-stable processes, and more recently $r$-Pareto processes, becoming the reference tools for the statistical analysis of…

Methodology · Statistics 2025-06-02 Peng Zhong , Scott A. Sisson , Boris Beranger

We prove a spectral upper bound for the torsion function of symmetric stable processes that holds for convex domains in $\mathbb{R}^d$. Our bound is explicit and captures the correct order of growth in $d$, improving upon the existing…

Probability · Mathematics 2021-10-19 Hugo Panzo

Grad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems, and thus the regularized models attain local well-posedness for Cauchy data. The hyperbolic regularization is only related to the…

Mathematical Physics · Physics 2017-03-24 Yana Di , Yuwei Fan , Ruo Li , Lingchao Zheng

The spatial Lambda-Fleming-Viot (SLFV) process (Barton, Etheridge and V\'eber, 2010) can be seen as a generalised Voter Model with configuration space $M^{R^d}$, where M is the set of probability measures on some space K. Such processes are…

Probability · Mathematics 2014-01-28 Habib Saadi

We construct a general stochastic process and prove weak convergence results. It is scaled in space and through the parameters of its distribution. We show that our simplified scaling is equivalent to time scaling used frequently. The…

Probability · Mathematics 2011-07-01 Mine Caglar

Aulbach et al. (2013) introduced a max-domain of attraction approach for extreme value theory in C[0,1] based on functional distribution functions, which is more general than the approach based on weak convergence in de Haan and Lin (2001).…

Probability · Mathematics 2014-12-12 Stefan Aulbach , Michael Falk , Martin Hofmann , Maximilian Zott

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…

Statistics Theory · Mathematics 2021-06-18 Phillip Murray , Riccardo Passeggeri , Almut E. D. Veraart , Mikko S. Pakkanen

We establish that if a sequence of spaces equipped with resistance metrics and measures converge with respect to the Gromov-Hausdorff-vague topology, and a certain non-explosion condition is satisfied, then the associated stochastic…

Probability · Mathematics 2016-09-20 D. A. Croydon

The result provided in this paper helps complete a unified picture of the scaling behavior in heavy-tailed stochastic models for transmission of packet traffic on high-speed communication links. Popular models include infinite source…

Probability · Mathematics 2010-08-17 Clément Dombry , Ingemar Kaj

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

Sup-normalized spectral functions form building blocks of max-stable and Pareto processes and therefore play an important role in modeling spatial extremes. For one of the most popular examples, the Brown-Resnick process, simulation is not…

Statistics Theory · Mathematics 2019-02-26 Marco Oesting , Martin Schlather , Claudia Schillings

We introduce a transform on the class of stochastic exponentials for d-dimensional Brownian motions. Each stochastic exponential generates another stochastic exponential under the transform. The new exponential process is often merely a…

Probability · Mathematics 2007-05-23 Victor Goodman