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We summarize significant classical results on (in)determinacy of measures in terms of their finite positive integer order moments. Well-known is the role of the smallest eigenvalues of Hankel matrices, starting from Hamburger's results a…
Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients are Dirichlet. A method is provided for calculating the distribution of these…
Economic and financial theories and practice essentially deal with uncertain future. Humans encounter uncertainty in different kinds of activity, from sensory-motor control to dynamics in financial markets, what has been subject of…
Continuous time random walks are non-Markovian stochastic processes, which are only partly characterized by single-time probability distributions. We derive a closed evolution equation for joint two-point probability density functions of a…
Power-law distributions are typical macroscopic features occurring in almost all complex systems observable in nature. As a result, researchers in quantitative analyses must often generate random synthetic variates obeying power-law…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
The $G$-expectation framework is a generalization of the classical probabilistic system motivated by Knightian uncertainty, where the $G$-normal plays a central role. However, from a statistical perspective, $G$-normal distributions look…
We revisit the moment method to obtain a slightly strengthened version of the usual semicircular law. Our version assumes only that the upper triangular entries of Hermitian random matrices are independent, have mean zero and variances…
We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…
Consider a $N\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are given by $Y_{ij}^{n}=\frac{\sigma(i/N,j/n)}{\sqrt{n}} X_{ij}^{n}$, the $X_{ij}^{n}$ being centered i.i.d. and $\sigma:[0,1]^2 \to (0,\infty)$ being a continuous…
Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…
We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which…
We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out…
The paper gives a parametrization of the solution set of a matricial Stieltjes-type truncated power moment problem in the non-degenerate and degenerate cases. The key role plays the solution of the corresponding system of Potapov's…
For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type…
We investigate moment sequences of probability measures on $E\subset\mathbb{R}$ under constraints of certain moments being fixed. This corresponds to studying sections of $n$-th moment spaces, i.e. the spaces of moment sequences of order…
In the world of multivariate extremes, estimation of the dependence structure still presents a challenge and an interesting problem. A procedure for the bivariate case is presented that opens the road to a similar way of handling the…
An important aspect of the shape of a distribution is the level of asymmetry. Strong asymmetries play a role in many ecosystems and are found in the size and reproductive success of individuals. But the standard third moment coefficient of…
Numerical solutions of stationary diffusion equations on the unit sphere with isotropic lognormal diffusion coefficients are considered. H\"older regularity in $L^p$ sense for isotropic Gaussian random fields is obtained and related to the…