相关论文: Critical Brownian multiplicative chaos
This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…
We handle divergent {\epsilon} expansions in different universality classes derived from modified Landau-Wilson Hamiltonian. Landau-Wilson Hamiltonian can cater for describing critical phenomena on a wide range of physical systems which…
A family of log-correlated Gaussian processes indexed by metric spaces is introduced, when the metric is conditionally negative definite. These processes arise as the limit of bi-fractional Brownian motions indexed by $(H,K)$ scaled by…
Brownian and fractional processes are useful computational tools for the modelling of physical phenomena. Here, modelling linear homopolymers in solution as Brownian or fractional processes, we develop a formalism to take into account both…
One of the tasks of the Bayesian inverse problem is to find a good estimate based on the posterior probability density. The most common point estimators are the conditional mean (CM) and maximum a posteriori (MAP) estimates, which…
The chaos expansion of a general non-linear function of a Gaussian stationary increment process conditioned on its past realizations is derived. This work combines Wiener chaos expansion approach to study the dynamics of a stochastic system…
Compressive sampling has been widely used for sparse polynomial chaos (PC) approximation of stochastic functions. The recovery accuracy of compressive sampling highly depends on the incoherence properties of the measurement matrix. In this…
We construct a family of invariant measures from the perspective of a shock in the KPZ fixed point. These measures are parameterized by a positive number $\theta > 0$, and are supported on functions $f$ satisfying $\lim_{|x| \to \infty}…
A noise reinforced Brownian motion is a centered Gaussian process $\hat B=(\hat B(t))_{t\geq 0}$ with covariance $E(\hat B(t)\hat B(s))=(1-2p)^{-1}t^ps^{1-p} \quad \text{for} \quad 0\leq s \leq t,$ where $p\in(0,1/2)$ is a reinforcement…
This paper establishes a functional law of large numbers and a functional central limit theorem for marked Hawkes point measures and their corresponding shot noise processes. We prove that the normalized random measure can be approximated…
We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…
In this article, we study the extremal processes of branching Brownian motions conditioned on having an unusually large maximum. The limiting point measures form a one-parameter family and are the decoration point measures in the extremal…
We introduce a set of tools which simplify and streamline the proofs of limit theorems concerning near-critical particles in branching random walks under optimal assumptions. We exemplify our method by giving another proof of the…
We describe generalized Brownian motion related to parabolic equation systems from a logical point of view, i.e., as a generalization of Anderson's random walk. The connection to classical spaces is based on the Loeb measure. It seems that…
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…
The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…
In this work, we explore an unconventional class of problems in the study of (quantum) critical phenomena, termed ''deep boundary criticality''. Traditionally, critical systems are analyzed with two types of perturbations: those uniformly…
We consider the gamma process perturbed by a Brownian motion (independent of the gamma process) as a degradation model. Parameters estimation is studied here. We assume that $n$ independent items are observed at irregular instants. From…
Bifractional Brownian motion (bfBm) is a centered Gaussian process with covariance \[ R^{(H,K)}(s,t)= 2^{-K} \left( \left(|s|^{2H}+|t|^{2H} \right)^{K}-|t-s|^{2HK}\right), \qquad s,t\in R. \] We study the existence of bfBm for a given pair…
Let $\mu_t$ denote the critical derivative Gibbs measure of branching Brownian motion at time $t$. It has been proved by Madaule (Stochastic Process. Appl. 126 (2016), no. 2, 470--502) and Maillard and Zeitouni (Ann. Inst. Henri Poincar\'e…