相关论文: Crystalline temperate distributions with uniformly…
The distribution of the sum of 1-dependent lattice vectors with supports on coordinate axes is approximated by a multivariate compound Poisson distribution and by signed compound Poisson measure. The local and $\ell_\alpha$-norms are used…
In this paper, we investigate the roles of compact sets in the space of tempered distributions $\mathscr{S}^{\prime}$. The key notion is "k-spaces", which constitute a fairly general class of topological spaces. In a k-space, the system of…
For functions from the set of generalized Poisson integrals $C^{\alpha,r}_{\beta}L_{p}$, $1\leq p <\infty$, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the…
This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and…
In this paper, we study the class of tempered distributions whose Fourier transform is a translation bounded measure and show that each such distribution in $\mathbb{R}^d$ has order at most $2d$. We show the existence of the generalized…
We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear…
We investigate the hydrodynamic behavior of zeroes of trigonometric polynomials under repeated differentiation. We show that if the zeroes of a real-rooted, degree $d$ trigonometric polynomial are distributed according to some probability…
By the method of Poissonization we confirm some existing results concerning consistent estimation of the structural distribution function in the situation of a large number of rare events. Inconsistency of the so called natural estimator is…
How can we draw trustworthy scientific conclusions? One criterion is that a study can be replicated by independent teams. While replication is critically important, it is arguably insufficient. If a study is biased for some reason and other…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…
Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
We observe thermal motions of ions, and molecules in water through light extinction, at the individual particle level. The motions appear as time dependent intensity variations, characterized through their averaged spectra. Theoretical…
One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on…
We derive spectral width estimates for traces of tempered solutions of a large class of multiplier equations in $\mathbf{R}^n$. The estimates are uniform for solutions up to a given order. In the process, we find a rather explicit…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…