Related papers: General alpha-Wiener bridges

Assuming the Riemann Hypothesis we study negative moments of the Riemann zeta-function and obtain asymptotic formulas in certain ranges of the shift in $\zeta(s)$. For example, integrating $|\zeta(1/2+\alpha+it)|^{-2k}$ with respect to $t$…

In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven…

We consider a discrete bridge from $(0,0)$ to $(2N,0)$ evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order $N^{-\alpha}$ with $\alpha \in (0,\infty)$. We provide a…

The Wigner's theorem, which is one of the cornerstones of the mathematical formulation of quantum mechanics, asserts that every symmetry of quantum system is unitary or anti-unitary. This classical result was first given by Wigner in 1931.…

We define the {\it Wirtinger number} of a link, an invariant closely related to the meridional rank. The Wirtinger number is the minimum number of generators of the fundamental group of the link complement over all meridional presentations…

I define and characterize the reweighted methods, which are techniques used in conjunction with the random series implementation of the Feynman-Kac formula. I prove several convergence results valid for all series representations and then I…

We consider the classical Wiener-Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known…

The aim of our work is to study vertex-reinforced jump processes with super-linear weight function $w(t) = t^\alpha$ , for some $\alpha>1$. On any complete graph $G = (V, E)$, we prove that there is one vertex $v \in V$ such that the total…

We study a generalization of the Brownian bridge as a stochastic process that models the position and velocity of inertial particles between the two end-points of a time interval. The particles experience random acceleration and are assumed…

This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…

We consider a branching random walk with an absorbing barrier, where the step of the associated one-dimensional random walk is in the domain of attraction of an $\alpha$-stable law with $1<\alpha<2$. We shall prove that there is a barrier…

In the paper we propose an universal bridge functional for the closure of the Ornstein-Zernike (OZ) equation for the case of infinitely diluted solutions of Lennard-Jones shperes of different size in the Lennard-Jones fluid. Bridge…

Let $x_\alpha$ be a net in a locally solid vector lattice $(X,\tau)$; we say that $x_\alpha$ is unbounded $\tau$-convergent to a vector $x\in X$ if $\lvert x_\alpha-x \rvert\wedge w \xrightarrow{\tau} 0$ for all $w\in X_+$. In this paper,…

We establish that Laplace transforms of the posterior Dirichlet process converge to those of the limiting Brownian bridge process in a neighbourhood about zero, uniformly over Glivenko-Cantelli function classes. For real-valued random…

Nonintersecting Brownian bridges on the unit circle form a determinantal stochastic process exhibiting random matrix statistics for large numbers of walkers. We investigate the effect of adding a drift term to walkers on the circle…

This paper considers the question of the rate of convergence to ${\alpha}$- stable laws, using arguments based on the Zolotarev distance to prove bounds. We provide a rate of convergence to ${\alpha}$-stable random variable where 1 <…

An explicit formula for the probability that a continuous local martingale crosses a one or two-sided random constant boundary in a finite time interval is derived. We obtain that the boundary crossing probability of a continuous local…

We consider in what sense quantum tunnelling is associated with non-classical probabilistic behaviour. We use the Wigner function quasi-probability description of quantum states. We give a definition of tunnelling that allows us to say…

We prove that an integrated simple random walk, where random walk and integrated random walk are conditioned to return to zero, has asymptotic probability $n^{-1/2}$ to stay positive. This question is motivated by so-called random polymer…

We consider a continuous-time Ehrenfest model defined over the integers from -N to N, and subject to catastrophes occurring at constant rate. The effect of each catastrophe instantaneously resets the process to state 0. We investigate both…