相关论文: Distributions of linear functionals of two paramet…
The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…
Nowadays, there is a series of complexities in biophysics that require a suitable approach to determine the measurable quantity. In this way, the superstatistics has been an important tool to investigate dynamic aspects of particles,…
We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is…
The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…
The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…
In this paper, we provide closed form expressions for the probability density functions (PDF) of the interference power in a network whose transmitters are arranged according to the Poisson Point Process (PPP). These expressions apply for…
The Mittag-Leffler function $E_{\alpha}$ being a natural generalization of the exponential function, an infinite-dimensional version of the fractional Poisson measure would have a characteristic functional \[ C_{\alpha}(\phi)…
In this paper a new lifetime distribution which is obtained by compounding Lindley and geometric distributions, named Lindley-geometric (LG) distribution, is introduced. Several properties of the new distribution such as density, failure…
We derive the probability distribution of product of two independent random variables, each distributed according the one-dimensional stable law. We represent the density by its power series and its asymptotic expansions. As Fox's…
This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailor-made to address inferential questions arising in a wide range of…
This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…
The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science, and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but not identically distributed…
We study the empirical process arising from a multi-dimensional diffusion process with periodic drift and diffusivity. The smoothing properties of the generator of the diffusion are exploited to prove the Donsker property for certain…
We introduce a new approach to absolute continuity of laws of Poisson functionals. It is based on the {\it energy image density} property for Dirichlet forms and on what we call {\it the lent particle method} which consists in adding a…
We identify stationary distributions of generalized Fleming-Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures…
We show the zero-density estimate \[ N(\zeta_{\mathcal{P}}; \alpha, T) \ll T^{\frac{4(1-\alpha)}{3-2\alpha-\theta}}(\log T)^{9} \] for Beurling zeta functions $\zeta_{\mathcal{P}}$ attached to Beurling generalized number systems with…
In this study we aim for a deeper understanding of the power law slope, $\alpha$, of waiting time distributions. Statistically independent events with linear behavior can be characterized by binomial, Gaussian, exponential, or Poissonian…
In this paper, we use a biorthogonal approach (Appell system) to construct and characterize the spaces of test and generalized functions associated to the fractional Poisson measure $\pi_{\lambda,\beta}$, that is, a probability measure in…
This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…
In this paper we consider the Riemann--Liouville fractional integral $\mathcal{N}^{\alpha,\nu}(t)= \frac{1}{\Gamma(\alpha)} \int_0^t (t-s)^{\alpha-1}N^\nu(s) \, \mathrm ds $, where $N^\nu(t)$, $t \ge 0$, is a fractional Poisson process of…