Related papers: Th\'{e}or\`{e}me de Donsker et formes de Dirichlet

In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result…

In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is…

We construct an almost sure bijection that recovers the directed landscape on the half-plane from a sequence of independent Brownian motions. This map is the natural scaling limit of the Robinson--Schensted--Knuth (RSK) correspondence. The…

We use recent results on the Fourier analysis of the zero sets of Brownian motion to explore the diophantine properties of an algorithmically random Brownian motion (also known as a complex oscillation). We discuss the construction and…

We study the probabilistic behaviour of the continued fraction expansion of a quadratic irrational number, when weighted by some "additive" cost. We prove asymptotic Gaussian limit laws, with an optimal speed of convergence. We deal with…

We consider the use of random walks as an approach to obtain connection coefficients for higher-order Bernoulli and Euler polynomials. In particular, we consider the cases of a $1$-dimensional linear reflected Brownian motion and of a…

We consider random walks on the square lattice of the plane along the lines of Heyde (1982, 1993) and den Hollander (1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics.…

We extend the functional Breuer-Major theorem by Nourdin and Nualart (2020) to the space of rough paths. The proof of tightness combines the multiplication formula for iterated Malliavin divergences, due to Furlan and Gubinelli (2019), with…

There are many classical random walk in random environment results that apply to ergodic random planar environments. We extend some of these results to random environments in which the length scale varies from place to place, so that the…

In this paper, we consider an ergodic Ornstein-Uhlenbeck process with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its jump intensity depend on unknown parameters.…

We are concerned with random walks on $\mathbb{Z}^d$, $d\geq 3$, in an i.i.d. random environment with transition probabilities $\epsilon$-close to those of simple random walk. We assume that the environment is balanced in one fixed…

We study random walks on sub-Riemannian manifolds using the framework of retractions, i.e., approximations of normal geodesics. We show that such walks converge to the correct horizontal Brownian motion if normal geodesics are approximated…

A reinforcement algorithm introduced by H.A. Simon \cite{Simon} produces a sequence of uniform random variables with memory as follows. At each step, with a fixed probability $p\in(0,1)$, $\hat U_{n+1}$ is sampled uniformly from $\hat U_1,…

We study rates of convergence in central limit theorems for the partial sum of squares of general Gaussian sequences, using tools from analysis on Wiener space. No assumption of stationarity, asymptotically or otherwise, is made. The main…

We prove invariance principles for a mulditimensional random walk conditioned to stay in a cone. Our first result concerns convergence towards the Brownian meander in the cone. Furthermore, we prove functional convergence of $h$-transformed…

Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory.…

We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart,…

We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…

The sample paths of Brownian motion are known to admit the exact Besov-type smoothness exponent 1/2 when measured in the sub-Gaussian Orlicz norm. We extend these regularity results by deriving the exact limit of the sub-Gaussian Orlicz…

We prove that random walks on a family of tilings of d-dimensional Euclidean space, with a canonical choice of conductances, converge to Brownian motion modulo time parameterization. This class of tilings includes Delaunay triangulations…