Related papers: On approximation rates for boundary crossing proba…
We investigate the large scale structure of certain sojourn sets of one dimensional Brownian motion within two-sided moving boundaries. The macroscopic Hausdorff dimension, upper mass dimension and logarithmic density of these sets are…
We consider optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a finite interval. Optimal stopping rules are found as the…
In this paper, we determine the Poisson boundary of the relativistic Brownian motion in two classes of Lorentzian manifolds, namely model manifolds of constant scalar curvature and Robertson--Walker space-times, the latter constituting a…
We study the probability of two Brownian particles to meet before one of them exits a finite interval. We obtain an explicit expression for the probability as a function of the initial distance of the two particles using the Weierstrass…
A uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains is established. Exact Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are given. Extensions…
Fractional Brownian motion is a Gaussian process x(t) with zero mean and two-time correlations <x(t)x(s)> ~ t^{2H} + s^{2H} - |t-s|^{2H}, where H, with 0<H<1 is called the Hurst exponent. For H = 1/2, x(t) is a Brownian motion, while for H…
A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work,…
Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important question arises around determining how long it takes the…
A regime-switching geometric Brownian motion is used to model a geometric Brownian motion with its coefficients changing randomly according to a Markov chain. In this work, we give a complete characterization of the recurrent property of…
The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer…
We establish an invariance principle connecting boundary random walks on $\mathbb N$ with Feller's Brownian motions on $[0,\infty)$. A Feller's Brownian motion is a Feller process on $[0,\infty)$ whose excursions away from the boundary $0$…
We consider a random walk on the support of a stationary simple point process on $R^d$, $d\geq 2$ which satisfies a mixing condition w.r.t.the translations or has a strictly positive density uniformly on large enough cubes. Furthermore the…
We investigate the limiting distribution of geometric Brownian motion conditional on its running maximum taking large values. We show that the conditional distribution of the geometric Brownian motion converges after a suitable…
We study the asymptotic probability that a random walk with heavy-tailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely…
We prove existence and uniqueness of solutions to the initial-boundary value problem for the Lifshitz--Slyozov equation (a nonlinear transport equation on the half-line), focusing on the case of kinetic rates with unbounded derivative at…
Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite…
We establish the discrete approximation to Brownian motion with varying dimension (BMVD in abbreviation) by random walks. The setting is very similar to that in [11], but here we use a different method allowing us to get rid the…
Given a survival distribution on the positive half-axis and a Brownian motion, a solution of the inverse first-passage problem consists of a boundary so that the first passage time over the boundary has the given distribution. We show that…
In this work we relate the density of the first-passage time of a Wiener process to a moving boundary with the three dimensional Bessel bridge process and a solution of the heat equation with a moving boundary. We provide bounds.
We establish high probability estimates on the eigenvalue locations of Brownian motion on the $N$-dimensional unitary group, as well as estimates on the number of eigenvalues lying in any interval on the unit circle. These estimates are…