Related papers: On the diameter of the stopped spider process

We introduce a class of iterated processes called $\alpha$-time Brownian motion for $0<\alpha \leq 2$. These are obtained by taking Brownian motion and replacing the time parameter with a symmetric $\alpha$-stable process. We prove a…

Consider a Brownian motion on the circumference of the unit circle, which jumps to the opposite point of the circumference at incident times of an independent Poisson process of rate $\lambda$. We examine the problem of coupling two copies…

We use Stein's method to obtain a bound on the distance between scaled $p$-dimensional random walks and a $p$-dimensional (correlated) Brownian Motion. We consider dependence schemes including those in which the summands in scaled sums are…

Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…

We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior…

The signature is a collection of iterated integrals describing the "shape" of a path. It appears naturally in the Taylor expansions of controlled differential equations and, as a consequence, is arguably the central object within rough path…

We consider, through PDE methods, branching Brownian motion with drift and absorption. It is well know that there exists a critical drift which separates those processes which die out almost surely and those which survive with positive…

Motivated by recent studies of record statistics in relation to strongly correlated time series, we consider explicitly the drawdown time of a Levy process, which is defined as the time since it last achieved its running maximum when…

We define what we call an on/off Brownian snake. We use this to construct on/off super Brownian motion recently introduced to the literature by Blath and Jacobi and which is a measure-valued branching process with a dormant state and an…

The d-inverse is a generalized notion of inverse of a stochastic process having a certain tendency of increasing expectations. Scaling limit of the d-inverse of Brownian motion with functional drift is studied. Except for degenerate case,…

This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson…

We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1044-1079] proved the tightness of the minimum centered around its mean value. We show that a convergence in law holds, giving…

Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs.…

We consider an irreducible pair $\mu \leq_c \nu$ of probability measures on $\mathbb{R}^d$ in convex order. In arXiv:2306.11019, Backhoff, Beiglb\"ock, Schachermayer and Tschiderer have shown that the Stretched Brownian Motion from $\mu$ to…

By a classical result of Gray, Neuhoff and Shields (1975) the $\bar\varrho$ distance between stationary processes is identified with an optimal stationary coupling problem of the corresponding stationary measures on the infinite product…

In this paper we study the diameter of the random graph $G(n,p)$, i.e., the the largest finite distance between two vertices, for a wide range of functions $p=p(n)$. For $p=\la/n$ with $\la>1$ constant, we give a simple proof of an…

We consider the limit behavior of a one-dimensional random walk with unit jumps whose transition probabilities are modified every time the walk hits zero. The invariance principle is proved in the scheme of series where the size of…

We discuss the compact support property of the rough super-Brownian motion constructed as a scaling limit of a branching random walk in static random environment. The semi-linear equation corresponding to this measure-valued process is the…

Let $W^H=\{W^H(t), t \in \rr\}$ be a fractional Brownian motion of Hurst index $H \in (0, 1)$ with values in $\rr$, and let $L = \{L_t, t \ge 0\}$ be the local time process at zero of a strictly stable L\'evy process $X=\{X_t, t \ge 0\}$ of…

The Paulsen problem is a basic open problem in operator theory: Given vectors $u_1, \ldots, u_n \in \mathbb R^d$ that are $\epsilon$-nearly satisfying the Parseval's condition and the equal norm condition, is it close to a set of vectors…