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Coronavirus. Covid-19. Pandemic. A urgent topic now both in the public media all around the world and in our daily conversations. Infected or not, it still contaminated our lives. It changed what we believed as „normal”. It divided our existence into „Befo ...
We consider three classes of linear differential equations on distribution functions, with a fractional order alpha is an element of [0; 1]. The integer case alpha = 1 corresponds to the three classical extreme families. In general, we show that there is a ...
Many decision problems in science, engineering, and economics are affected by uncertainty, which is typically modeled by a random variable governed by an unknown probability distribution. For many practical applications, the probability distribution is onl ...
Ambient concentrations of ice-forming particles measured during ship expeditions are collected and summarised with the aim of determining the spatial distribution and variability in ice nuclei in oceanic regions. The presented data from literature and prev ...
The aim of this review-style paper is to provide a concise, self-contained and unified presentation of the construction and main properties of Gaussian multiplicative chaos (GMC) measures for log-correlated fields in 2D in the subcritical regime. By consid ...
Both numerical simulations and data-driven methods have been applied in dam's displacement modeling. For monitored displacement data-driven methods, the physical mechanism and structural correlations were rarely discussed. In order to take the spatial and ...
A well-known first-order method for sampling from log-concave probability distributions is the Unadjusted Langevin Algorithm (ULA). This work proposes a new annealing step-size schedule for ULA, which allows to prove new convergence guarantees for sampling ...
The standard practice in Generative Adversarial Networks (GANs) discards the discriminator during sampling. However, this sampling method loses valuable information learned by the discriminator regarding the data distribution. In this work, we propose a co ...
In this article we study imaginary Gaussian multiplicative chaos-namely a family of random generalized functions which can formally be written as e(iX(x)), where X is a log-correlated real-valued Gaussian field on R-d, that is, it has a logarithmic singula ...
Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...
