Heavy traffic models for wireless queueing systems under short range dependence and light tail assumptions on the data traffic have been studied recently. We outline one such model considered by Buche and Kushner [7]. At the same time, similarly to what happened for wireline networks, the emergence of high capacity applications (multimedia, gaming) and inherent mechanisms (multi-access interfer...

Tempered fractional Brownian motion is obtained when the power law kernel in the moving average representation of a fractional Brownian motion is multiplied by an exponential tempering factor. This paper develops the theory of stochastic integrals for tempered fractional Brownian motion. Along the way, we develop some basic results on tempered fractional calculus.

Brownian motion experiments have become a staple of the undergraduate advanced laboratory, yet quantification of these experiments is difficult, typically producing errors of 10%–15% or more. Here, we discuss the individual sources of error in the experiment: sampling error, uncertainty in the diffusion coefficient, tracking error, vibration, and microscope drift. We model each source of error ...

We provide a method for the generation of paths of Lévy processes which has many of the benefits that the Brownian bridge construction has for Brownian motion. We show how, using our method, one can apply stratified sampling and quasi-Monte Carlo methods to obtain better numerical schemes analog to the Brownian case. As a numerical example we consider the problem of pricing an asian option in t...

We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion. This provides a short proof of the recent result due to P. Carr et al [7] that the arithmetic average of geometric Brownian motion is increasing in the convex order. The Brownian sheet plays an essential role in the construction. Our method may also be applied when the Brownian motion ...

Brownian particles, mind the speedcam! It is now possible to measure the instantaneous speed of a Brownian particle. Not only are these measurements of fundamental importance for statistical physics, they also open up new perspectives for the study of quantum systems. " Mind the speedcam if you want to avoid a fine! ". Brownian particles must have surely taken heed of this warning, since, until...

We construct a Brownian path conditioned on its minimum value over a xed time interval by simple transformations of a Brownian bridge. Path transformations have proved useful in the study of Brownian motion and related processes , by providing simple constructions of various conditioned processes such as Brownian bridge, meander and excursion, starting from an unconditioned Brownian motion. As ...

Several Brownian areas are considered in this paper: the Brownian excursion area, the Brownian bridge area, the Brownian motion area, the Brownian meander area, the Brownian double meander area, the positive part of Brownian bridge area, the positive part of Brownian motion area. We are interested in the asymptotics of the right tail of their density function. Inverting a double Laplace transfo...

One century after Einstein's work, Brownian motion still remains both a fundamental open issue and a continuous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic approaches proposed in the literature to model the Brownian motion and more general diffusive behaviors. Then, we focus on the problems concerning the determinati...