Area Distribution of Elastic Brownian Motion

The first-passage area for drifted Brownian motion and the moments of the Airy distribution

An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis leads to a simple closed-form solution for the moments of the Airy distribution. PACS numbers: 02.50.-r, 05.40.-a, 05.40.Jc Short title: First-passa...

Tail Estimates for the Brownian Excursion Area and Other Brownian Areas

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...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Area of Brownian Motion with Generatingfunctionology

The distribution of the (absolute) area of Brownian motion was first studied by Mark Kac [Kac (1949)], using a formula since known as the Feynman–Kac formula [Kac (1949); Ito and McKean (1965)], which allows us to find the double Laplace transform of the distribution of the integral of a functional of Brownian motion. The area functional has received intensive attention for different types of B...

CFD simulations on natural convection heat transfer of alumina-water nanofluid with Brownian motion effect in a 3-D enclosure

The CFD simulation has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosure, whose dimension, width height length (mm), is 40 40 90, respectively. The nanofluid used in the present study is -water with various volumetric fractions of the alumina nanoparticles ranging from 0-3%. The Rayleigh number is . Fluent v6.3 is used to simulate nanofluid ...