Related papers: Scaling limits of nonlinear functions of random gr…

Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors,…

We implement a well-established concept to consider dispersion effects within a Poisson-Boltzmann approach of continuum solvation of proteins. The theoretical framework is particularly suited for boundary element methods. Free parameters…

We study analytically and numerically the problem of a nonlinear mechanical oscillator with additive noise in the absence of damping. We show that the amplitude, the velocity and the energy of the oscillator grow algebraically with time.…

We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on $\mathbb{Z}$, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the…

We consider the Boolean model $Z$ on $\mathbb{R}^d$ with random compact grains, i.e. $Z := \bigcup_{i \in \mathbb{N}} (X_i + Z_i)$ where $\eta_t := \{X_1, X_2, \dots\}$ is a Poisson point process of intensity $t$ and $(Z_1, Z_2, \dots)$ is…

Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence that can have long-range dependence. In this paper, we find the scaling limit of a random walk that follows GBP. The result is a new class of…

Let $\eta_t$ be a Poisson point process of intensity $t\geq 1$ on some state space $\Y$ and $f$ be a non-negative symmetric function on $\Y^k$ for some $k\geq 1$. Applying $f$ to all $k$-tuples of distinct points of $\eta_t$ generates a…

We derive the scaling function for the one dimensional noisy Burgers equation in the two-soliton approximation within the weak noise canonical phase space approach. The result is in agreement with an earlier heuristic expression and…

We study the Poisson Boolean model where the grains are random convex bodies with a rotation-invariant distribution. We say that a grain distribution is dense if the union of the grains covers the entire space and robust if the union of the…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of…

The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…

Let $\{\eta_i\}_{i\ge 1}$ be a sequence of dependent Bernoulli random variables. While the Poisson approximation for the distribution of $\sum_{i=1}^n\eta_i$ has been extensively studied in the literature, this paper establishes new…

The scaling behavior of the order parameter at the chiral phase transition, the so-called magnetic equation of state, of strongly interacting matter is studied within effective models. We explore universal and nonuniversal structures near…

The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…

We investigate the statistical properties of one-dimensional Burgers dynamics evolving from stochastic initial conditions defined by a Poisson point process for the velocity potential, with a power-law intensity. Thanks to the geometrical…

We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. We assume that the intensity of each Poisson process is of the form $s (\cdot, x)$ where $x$ is the covariate and where $s$ is an…

In a previous work, two of the authors proposed a new proof of a well known convergence result for the scaled elementary connected vacant component in the high intensity Boolean model towards the Crofton cell of the Poisson hyperplane…

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

Nonlinear relationships between covariates and a response variable of interest are frequently encountered in animal science research. Within statistical models, these nonlinear effects have, traditionally, been handled using a range of…