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We prove Berry-Esseen theorems, almost sure invariance principle rates and large deviations for products of independent but not identically distributed invertible matrices with some average (logarithmic) projective contraction and uniform…
In this paper we prove a strong law of large numbers and its L^1-convergence counterpart for the process counted with a random characteristic in the context of self-similar fragmentation processes. This result extends a somewhat analogical…
There has been a resurgence of interest in incomplete U-statistics that only sum over a subset of kernel evaluations, due to their computational efficiency and asymptotic normality which can be leveraged to quantify the uncertainty of…
In nature or societies, the power-law is present ubiquitously, and then it is important to investigate the mathematical characteristics of power-laws in the recent era of big data. In this paper we prove the superposition of non-identical…
We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…
This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable…
We give new evidence that quantum computers -- moreover, rudimentary quantum computers built entirely out of linear-optical elements -- cannot be efficiently simulated by classical computers. In particular, we define a model of computation…
The objective of this study is to investigate the limiting behavior of a subgraph counting process. The subgraph counting process we consider counts the number of subgraphs having a specific shape that exist outside an expanding ball as the…
Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…
We consider random multiplicative functions taking the values $\pm 1$. Using Stein's method for normal approximation, we prove a central limit theorem for the sum of such multiplicative functions in appropriate short intervals.
We consider a 2D stochastic wave equation driven by a Gaussian noise, which is temporally white and spatially colored described by the Riesz kernel. Our first main result is the functional central limit theorem for the spatial average of…
In order to characterize the fluctuation between the ergodic limit and the time-averaging estimator of a full discretization in a quantitative way, we establish a central limit theorem for the full discretization of the parabolic stochastic…
We prove a Berry-Esseen type inequality for approximating expectations of sufficiently smooth functions $f$, like $f=|\cdot|^3$, with respect to standardized convolutions of laws $P_1,\ldots, P_n$ on the real line by corresponding…
This paper discusses new methods for processing images in the photon-limited regime where the number of photons per pixel is binary. We present a new Bayesian denoising method for binary, single-photon images. Each pixel measurement is…
Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…
This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in…
The asymptotic behaviour of a closed BCMP network, with $n$ queues and $m_n$ clients, is analyzed when $n$ and $m_n$ become simultaneously large. Our method relies on Berry-Esseen type approximations coming in the Central Limit Theorem. We…
A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…