in this paper, we introduce an efficient method based on haar wavelet to approximate a solutionfor the two-dimensional linear stochastic fredholm integral equation. we also give an example to demonstrate the accuracy of the method.

in this paper, we show that the conditional transform with respect to the gaussian process involving the first variation can be expressed in terms of the conditional transform without the first variation. we then use this result to obtain various integration formulas involving the conditional $diamond$-product and the first variation.

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 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 ...

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process ...

this article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (mhd) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. the model used for the nanofluid incorporates the effects of brownian motion and thermophoresis in the presence of thermal radiation. the skin-friction coefficient, nusselt number an...

langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. the brownian motion generated from molecular bombardment was taken as a wiener stochastic process and approximated by a gaussian white noise. euler-maruyama method was used to solve the langevin equation numerically. the accuracy of brownian simulation was checked by performing a series of simulati...

G-Brownian motion has a very rich and interesting new structure that nontrivially generalizes the classical Brownian motion. Its quadratic variation process is also a continuous process with independent and stationary increments. We prove a self-normalized functional central limit theorem for independent and identically distributed random variables under the sub-linear expectation with the limi...