Related papers: Small parts in the Bernoulli sieve
For branching processes, the generating functions for limit distributions of so-called ratios of probabilities of rare events satisfy the Schr\"oder-type integral-functional equations. Excepting limited special cases, the corresponding…
Glitching pulsars fall broadly into two statistical classes: those with Poisson-like waiting times and power-law sizes, and those with unimodal waiting times and sizes. Previous glitch modeling based on a state-dependent Poisson process…
We consider a generalized version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line. We specify the distribution of the space of…
We consider a one-dimensional piecewise deterministic Markov process (PDMP) on $[0,1]$ with resetting at $0$ and depending on a small parameter $\varepsilon>0$. In the singular vanishing limit $\varepsilon \to 0$ we prove that the ``…
We propose a Bayesian approach to learn discriminative dictionaries for sparse representation of data. The proposed approach infers probability distributions over the atoms of a discriminative dictionary using a Beta Process. It also…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…
The limiting behavior of stochastic evolution processes with small noise intensity $\epsilon$ is investigated in distribution-based approach. Let $\mu^{\epsilon}$ be stationary measure for stochastic process $X^{\epsilon}$ with small…
We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process…
As a supplement of our previous work, we consider the localized region of the random Schroedinger operators on $l^2({\bf Z}^d)$ and study the point process composed of their eigenvalues and corresponding localization centers. For the…
We consider a point process $i+\xi_i$, where $i\in \bZ$ and the $\xi_{i}$'s are i.i.d. random variables with variance $\sigma^{2}$. This process, with a suitable rescaling of the distribution of $\xi_i$'s, converges to the Poisson process…
In this article we contribute to the moment analysis of branching processes in catalytic media. The many-to-few lemma based on the spine technique is used to derive a system of (discrete space) partial differential equations for the number…
The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke different spiking patterns at each trial. Probabilistic methods are essential to understand the functional role of this variance within…
In the seminal contribution [4] the joint weak convergence of maxima and minima of weakly dependent stationary sequences is derived under some mild asymptotic conditions. In this paper we address additionally the case of incomplete samples…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
We prove a Functional Central Limit Theorem for the position of a Tagged Particle in the one-dimensional Asymmetric Simple Exclusion Process in the hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle…
The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…
Given a homogeneous Poisson process on ${\mathbb{R}}^d$ with intensity $\lambda$, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that…
This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…