Related papers: Fractional calculus approach to the statistical ch…
The invariant is one of central topics in science, technology and engineering. The differential invariant is essential in understanding or describing some important phenomena or procedures in mathematics, physics, chemistry, biology or…
Attributes which are infrequently expressed in a population can require weeks or months of counting to reach statistical significance. But replacement in a stable population increases long-term counts to a degree determined by the…
We reconsider the Moran model in continuous time with population size $N$, two allelic types, and selection. We introduce a new particle representation, which we call the labelled Moran model, and which has the same distribution of type…
Advances in neural variational inference have facilitated the learning of powerful directed graphical models with continuous latent variables, such as variational autoencoders. The hope is that such models will learn to represent rich,…
Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…
Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…
Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for…
In mathematical finance and other applications of stochastic processes, it is frequently the case that the characteristic function may be known but explicit forms for density functions are not available. The simulation of any distribution…
Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schr\"odinger Equation containing a fractional…
We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool…
Physical and mathematical applications of fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we…
The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus…
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…
The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
The present paper proposes a robust evaluation of any radial density at small distances using negative-order radial moments evaluated in momentum space. This evaluation provides a valuable insight into the behavior of a given radial density…
This article introduces a novel method for detecting distinctive structural changes in economic data, particularly within frequency distribution tables. The approach identifies significant shifts in the distribution of a variable over time…
We show that the kinetic approach to statistical mechanics permits an elegant and efficient treatment of fractional exclusion statistics. By using the exclusion-inclusion principle recently proposed [Phys. Rev. E49, 5103 (1994)] as a…
This paper is devoted to the study of a fractional version of non-linear $\mathpzc{M}^\nu(t)$, $t>0$, linear $M^\nu (t)$, $t>0$ and sublinear $\mathfrak{M}^\nu (t)$, $t>0$ death processes. Fractionality is introduced by replacing the usual…