An identity in distribution due to F. Knight for Brownian motion is extended in two di erent ways: rstly by replacing the supremum of a re ecting Brownian motion by the range of an unre ected Brownian motion, and secondly by replacing the re ecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excurs...

An identity in distribution due to F. Knight for Brownian motion is extended in two diierent ways: rstly by replacing the supremum of a reeecting Brownian motion by the range of an unreeected Brownian motion, and secondly by replacing the reeecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excurs...

It has been demonstrated that Brownian models are effective for approximate analysis of queueing networks, particularly when no explicit analytical methods are available [3,4,1]. In 1988 Harrison [2] proposed Brownian models as approximations for multiclass open queueing networks. That work was expanded by Harrison and Nguyen in two recent papers [3,4] with the aim of developing a systematic me...

In this paper, we develop Brownian motion and discuss its basic properties. We then turn our attention to the “size” of Brownian motion by defining Hausdorff dimension and its relationship to Brownian motion. This leads to the final result of the paper that for n ≥ 2, both the range and graph of Brownian motion have Hausdorff dimension 2.

MHD boundary layer flow of two phase model nanofluid over a vertical plate is investigated both analytically and numerically. A system of governing nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations by suitable similarity transformations and then solved analytically using homotopy analysis method and numerically by the fourth order Rung...

The main goal of this paper is to present an explicit capacity estimate for hitting probabilities of the Brownian sheet. As applications, we determine the escape rates of the Brownian sheet, and also obtain a local intersection equivalence between the Brownian sheet and the additive Brownian motion. Other applications concern quasi{sure properties in Wiener space.

The main goal of this paper is to present an explicit capacity estimate for hitting probabilities of the Brownian sheet. As applications, we determine the escape rates of the Brownian sheet, and also obtain a local intersection equivalence between the Brownian sheet and the additive Brownian motion. Other applications concern quasi–sure properties in Wiener space.

Brownian motion of particles affects many branches of science. We report on the Brownian motion of micrometer-sized beads of glass held in air by an optical tweezer, over a wide range of pressures, and we measured the instantaneous velocity of a Brownian particle. Our results provide direct verification of the energy equipartition theorem for a Brownian particle. For short times, the ballistic ...

We present a decomposition of the sub-fractional Brownian motion into the sum of a fractional Brownian motion plus a stochastic process with absolutely continuous trajectories. The first application we show of this decomposition is the relation between the spaces of integrable functions with respect each one of these three processes. A general result of weak convergence to integrals of L(R) fun...