相关论文: Dispersion measure for symmetric, stable probabili…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival…
Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested…
We obtain a general solution for the probability density function of wave intensities in non-stationary Wave Turbulence. The solution is expressed in terms of the wave action spectrum evolving according the the wave-kinetic equation. We…
The article presents a novel variational calculus to analyze the stability and the propagation of chaos properties of nonlinear and interacting diffusions. This differential methodology combines gradient flow estimates with backward…
We study the probabilistic behavior of persistence-based statistics and propose a novel nonparametric framework for detecting structural changes in high-dimensional random point clouds. We establish moment bounds and tightness results for…
Richardson's theory of turbulent particle pair diffusion [Richardson, L. F. Proc. Roy. Soc. Lond. A 100, 709--737, 1926], based upon observational data, is equivalent to a locality hypothesis in which the turbulent pair diffusivity $(K)$…
A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in…
This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…
The study of distributed order calculus usually concerns about fractional derivatives of the form $\int_0^1 \partial^\alpha u \, m(d\alpha)$ for some measure $m$, eventually a probability measure. In this paper an approach based on L\'evy…
Statistical solutions of incompressible Euler describe turbulent dynamics as time-parameterized laws on $L^2$ whose multi-point correlations satisfy an infinite hierarchy of weak identities. Modern generative samplers for PDE forecasting…
Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…
We study local power fluctuations in numerical simulations of stationary, homogeneous, isotropic turbulence in two and three dimensions with Gaussian forcing. Due to the near-Gaussianity of the one-point velocity distribution, the…
We study evolution equations of drift-diffusion type when various parameters are random. Motivated by applications in pedestrian dynamics, we focus on the case when the total mass is, due to boundary or reaction terms, not conserved. After…
The probability density function (PDF) of velocity fluctuations is studied experimentally for grid turbulence in a systematical manner. At small distances from the grid, where the turbulence is still developing, the PDF is sub-Gaussian. At…
Observations of radio signals from distant pulsars provide a valuable tool for investigation of interstellar turbulence. The time-shapes of the signals are the result of pulse broadening by the fluctuating electron density in the…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
The Lagrangian statistics of relative dispersion in fully developed turbulence is numerically investigated. A scaling range spanning many decades is achieved by generating a synthetic velocity field with prescribed Eulerian statistical…