相关论文: Inter-arrival time distribution for the non-homoge…

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…

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, and the approximation error, as measured in…

An asymptotic expansion for inverse moments of positive binomial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribution. Compared to previous…

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…

We deduce the non-asymptotical bilateral estimates for moment inequalities for sums of non-negative independent random variables, based on the correspondent estimates for the so-called Bell functions and the Poisson distribution.

We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we…

Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional…

We consider an elliptic and time-inhomogeneous diffusion process with time-periodic coefficients evolving in a bounded domain of $\mathbb{R}^d$ with a smooth boundary. The process is killed when it hits the boundary of the domain (hard…

We review the properties of time intervals between the crossings at a level M of a smooth stationary Gaussian temporal signal. The distribution of these intervals and the persistence are derived within the Independent Interval Approximation…

A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $[n]=\{1,...,n\}$ at time $\theta \ge 0$ is governed by the Ewens sampling formula with parameter $\theta$. These…

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based…

This paper addresses a detection problem where several spatially distributed sensors independently observe a time-inhomogeneous stochastic process. The task is to decide between two hypotheses regarding the statistics of the observed…

A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson…

Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of…

This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…

Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity…

Prediction of events such as part replacement and failure events plays a critical role in reliability engineering. Event stream data are commonly observed in manufacturing and teleservice systems. Designing predictive models for individual…

Multiparticle production processes in $pp$ collisions at the central rapidity region are usually considered to be divided into independent "soft" and "hard" components. The first is described by exponential (thermal-like) transverse…

In a discrete-time setting, we consider an arrival process $\left\{\xi_n \, \middle| \, n = 1, 2, \ldots \right\}$, which models the occurrence of events, and a corresponding point process $\left\{H_n \, \middle| \, n = 1, 2, \ldots…

The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…