相关论文: Dispersion measure for symmetric, stable probabili…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
Taylor diffusion (or dispersion) refers to a phenomenon discovered experimentally by Taylor in the 1950s where a solute dropped into a pipe with a background shear flow experiences diffusion at a rate proportional to $1/\nu$, which is much…
In this paper, the statistical properties of Newton s method algorithm output in a specific case have been studied. The relative frequency density of this sample converges to a well-defined function, prompting us to explore its…
We study stability of the sharp Poincar{\'e} constant of the invariant probability measure of a reversible diffusion process satisfying some natural conditions. The proof is based on the spectral interpretation of Poincar{\'e} inequalities…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
We trace a conceptual genealogy from Abraham de Moivre's derivation of the normal curve (1733) to the modern distributional approach to statistics. De Moivre's Approximatio ad Summam Terminorum Binomii gave the first systematic derivation…
Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory. This theory describes the geometric features of the statistical manifold $\mathcal{M}$ of random events that are described by a…
This paper is devoted to a statistical analysis of the fluctuations of velocity and acceleration produced by a random distribution of point vortices in two-dimensional turbulence. We show that the velocity probability density function…
The absorption of acoustic wave propagation in a broad variety of lossy media is characterized by an empirical power law function of frequency, w^y. It has long been noted that exponent y ranges from 0 to 2 for diverse media. Recently, the…
We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…
We introduce the notion of symmetric covariation, which is a new measure of dependence between two components of a symmetric $\alpha$-stable random vector, where the stability parameter $\alpha$ measures the heavy-tailedness of its…
We study the process of dispersion of low-regularity solutions to the Schr\"odinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
In this article, we first review the connection between L\'evy processes and infinitely divisible random variables, and the classification of infinitely divisible distributions. Using this connection and the L\'evy-Khinchine representation…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
An important family of structural constants in the theory of symmetric functions and in the representation theory of symmetric groups and general linear groups are the plethysm coefficients. In 1950, Foulkes observed that they have some…
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…
Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference. However, the error analysis for discrete diffusion models remains less well-understood. In…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…