相关论文: Poisson limit of an inhomogeneous nearly critical …

The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here…

We study the binary classification problem for Poisson point processes, which are allowed to take values in a general metric space. The problem is tackled in two different ways: estimating nonparametricaly the intensity functions of the…

We study the facilitated totally asymmetric exclusion process on the one dimensional integer lattice. We investigate the invariant measures and the limiting behavior of the process. We mainly derive the limiting distribution of the process…

We present sufficient conditions for sums of dependent point processes to converge in distribution to a Poisson process. This extends the classical result of Grigelionis [Theory Probab. Appl. 8 (1963) 172--182] for sums of uniformly null…

This paper proposes a piecewise autoregression for general integer-valued time series. The conditional mean of the process depends on a parameter which is piecewise constant over time. We derive an inference procedure based on a penalized…

A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…

Integer-valued time series models have been a recurrent theme considered in many papers in the last three decades, but only a few of them have dealt with models on $\mathbb Z$ (that is, including both negative and positive integers). Our…

We consider a discrete-time version of a Hawkes process defined as a Poisson auto-regressive process whose parameters depend on the past of the trajectory. We allow these parameters to take on negative values, modelling inhibition. More…

The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinitely imbalanced. In this paper, it is shown that this phenomenon is universal in a wide class of link functions on…

The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…

We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…

We study the statistical limits of both detecting and estimating a rank-one deformation of a symmetric random Gaussian tensor. We establish upper and lower bounds on the critical signal-to-noise ratio, under a variety of priors for the…

In this paper, we consider the normalized least squares estimator of the parameter in a mildly-explosive first-order autoregressive model with dependent errors which are modeled as a mildly-explosive AR(1) process. We prove that the…

In this paper we establish lower bounds on information divergence of a distribution on the integers from a Poisson distribution. These lower bounds are tight and in the cases where a rate of convergence in the Law of Thin Numbers can be…

We consider the problem of threshold estimation for autoregressive time series with a "space switching" in the situation, when the regression is nonlinear and the innovations have a smooth, possibly non Gaussian, probability density.…

In this paper, we consider the Poisson equation on a "long" domain which is the Cartesian product of a one-dimensional long interval with a (d-1)-dimensional domain. The right-hand side is assumed to have a rank-1 tensor structure. We will…

The stochastic processes of finite length defined by recurrence relations request additional relations specifying the first terms of the process analogously to the initial conditions for the differential equations. As a general rule, in…

The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain, and combinations of these. For…

We consider the Gibbs measure of a general interacting particle system for a certain class of ``weakly interacting" kernels. In particular, we show that the local point process converges to a Poisson point process as long as the inverse…

Extreme values are considered in samples with random size that has a mixed Poisson distribution being generated by a doubly stochastic Poisson process. We prove some inequalities providing bounds on the rate of convergence in limit theorems…