Nowadays, microchannels as closed circuits channels for fluid flow and heat removal are an integral part of the silicon-based electronic microsystems. Most of previous numerical studies on microchannel heat sinks (MCHS) have been performed for a two-dimensional domain using constant properties of the working fluid. In this study, laminar fluid flow and heat transfer of variable properties Al2O3...

An 'oscillating' version of Brownian motion is defined and studied. 'Ordinary' Brownian motion and 'reflecting' Brownian motion are shown to arise as special cases. Transition densities, first-passage time distributions, and occupation time distributions for the process are obtained explicitly. Convergence of a simple oscillating random walk to an oscillating Brownian motion process is establis...

The paper deals with a path-valued Markov process: the re ecting Brownian snake. It is a particular case of the path-valued process previously introduced by Le Gall. Here the spatial motion is a re ecting Brownian motion in a domain D of R. Using this probabilistic tool, we construct an explicit function v solution of an integral equation which is, under some hypotheses on the regularity of v, ...

In this paper, we present the fundamental framework of the evaluation problem under which the evaluation operator satisfying some axioms is linear. Based on the dynamic linear evaluation mechanism of contingent claims, studying this evaluation rule in the market driven by fractional Brownian motions has led to a dynamic capital asset pricing model. It is deduced here mainly with the fractional ...

Abstract. Moderate deviation principles are established in dimensions d ≥ 3 for the super Brownian motion with random immigration X t , where the immigration rate is governed by the trajectory of another super-Brownian motion %. It fills in the gap between the central limit theorem and the large deviation principles for this model which obtained by Hong & Li (1999) and Hong (2001).

The traffic patterns of today’s IP networks exhibit two important properties: self-similarity and long-range dependence. The fractional Brownian motion is widely used for representing the traffic model with the properties. We consider a single server fluid queueing system with input process of a fractional Brownian motion type. Formulas for effective bandwidth are derived in a single source and...