Let X be a Brownian motion defined on the line (with X(0)=0) and let Y be an independent Brownian motion defined on the nonnegative real numbers. For all t ≥ 0, we define the iterated Brownian motion (IBM), Z, by setting Z t ∆ = X(Y t). In this paper we determine the exact uniform modulus of continuity of the process Z.

We show that Pitman’s theorem relating Brownian motion and the BES(3) process, as well as the Ray-Knight theorems for Brownian local times remain valid, mutatis mutandis, under the limiting laws of Brownian motion penalized by a function of its one-sided maximum.

In this paper we investigate three discrete or semi-discrete approximation schemes for reflected Brownian motion on bounded Euclidean domains. For a class of bounded domains D in R that includes all bounded Lipschitz domains and the von Koch snowflake domain, we show that the laws of both discrete and continuous time simple random walks on D ∩ 2Z moving at the rate 2 with stationary initial dis...

In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empiric...

In this paper, we consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. We show that we can describe the evolution of the distance between the two processes with a stochastic differential equation. This S.D.E. possesses a jump component driven by the excursion process of one of the two skew Brownian motions. U...

1 Brownian Motion in Cells Description (BMC) 2 The Browian Motion in Cells Experiment Photos 3 Before the 1st Day of Lab Objectives for this experiment 4 Introduction 4.1 Brownian Motion 4.2 Intracellular Transport 4.3 Experimental Setup and supply list 4.4 Supplies Used in this experiment 4.5 Experiment Timeline 4.5.1 On your first day in the lab 4.5.2 On your second day in the lab 4.5.3 On da...

Renewal-anomalous-heterogeneous files are solved. A simple file is made of Brownian hard spheres that diffuse stochastically in an effective 1D channel. Generally, Brownian files are heterogeneous: the spheres’ diffusion coefficients are distributed and the initial spheres’ density is non-uniform. In renewal-anomalous files, the distribution of waiting times for individual jumps is exponential ...

Let B = {(B1 t , . . . , Bd t ) , t ≥ 0} be a d-dimensional fractional Brownian motion with Hurst parameter H and let Rt = √ (B1 t ) 2 + · · · + (Bd t )2 be the fractional Bessel process. Itô’s formula for the fractional Brownian motion leads to the equation Rt = ∑d i=1 ∫ t 0 Bi s Rs dBi s + H(d − 1) ∫ t 0 s2H−1 Rs ds . In the Brownian motion case (H = 1/2), Xt = ∑d i=1 ∫ t 0 Bi s Rs dBi s is a...

For the GI0GI01 queue we show that the scaled queue size converges to reflected Brownian motion in a critical queue and converges to reflected Brownian motion with drift for a sequence of subcritical queuing models that approach a critical model+ Instead of invoking the topological argument of the usual continuousmapping approach, we give a probabilistic argument using Skorokhod embeddings in B...