The present analysis deals with an unsteady magnetohydrodynamic flow of Eyring-Powell nanofluid over an inclined permeable stretching sheet. Effects of thermal radiation, Joule heating, and chemical reaction are considered. The effects of Brownian motion and thermophoresis on the flow over the permeable stretching sheet are discussed. Using Runge-Kutta fourth-order along with shooting technique...

A Brownian ratchet is a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. A flashing Brownian ratchet is a process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, producing directed motion. These processes have been of interest to physicists and biologists for nearly 25 years. The flashing ...

The present investigation draws scholars' attention to the effect of exponential variable viscosity modeled by Vogel and variable permeability on stagnation point flow of Carreau Nanofluid over an electromagnetic plate through a porous medium. Brownian motion and thermophoretic diffusion mechanism are taken into consideration. An efficient fourth-order RK method along with shooting technique ar...

Skew Brownian motion was introduced by Itô and Mckean 1 to furnish a construction of certain stochastic processes related to Feller’s classification of second-order differential operators associated with diffusion processes see also Section 4.2 in 2 . For α ∈ 0, 1 , the α-skew Brownian motion is defined as a one-dimensional Markov process with the same transition mechanism as of the usual Brown...

We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domainD is killed; at the same time, a different particle splits into two particles. For large N , the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge...

Consider a complete probability space (Ω,F ,P;F) equipped with the Þltration F = {Ft; 0 ≤ t <∞}. A stochastic process is a collection of random variables X = {Xt; 0 ≤ t <∞} where, for every t, Xt : Ω → Rd is a random variable. We assume the space Rd is equipped with the usual Borel σ-algebra B(Rd). Every Þxed ω ∈ Ω corresponds to a sample path (or, trajectory), that is, the function t 7→ Xt(ω) ...

The (linear, separable) Brownian motion process has been studied more than any other stochastic process. It has many applications and, at least since Bachelier, probabilists have been at(tract,ed by its delicate and curious properties. It furnished, in the hands of N. Jyiener, the first instance of a satisfactorily defined nondiscrete stochastic process n-ith continuous time parameter, and it i...

We study some path transformations related to Pitman’s theorem on Brownian motion and the three dimensional Bessel process. We relate these to Littelmann path model, and give applications to representation theory and to Brownian motion in a Weyl chamber.

In one way or another, the extension of the standard Brownian motion process {B¡: t e [0,oo)} to a (Gaussian) random field {Bt: t € R+} involves a proof of the positive semi-definiteness of the kernel used to generalize p(s, 1) = cov(Bs,B¡) = s A t to multidimensional time. Simple direct analytical proofs are provided here for the cases of (i) the Levy multiparameter Brownian motion, (ii) the C...

We show that Pitman’s theorem relating Brownian motion and the BES(3) process, as well as the Ray-Knight theorems for Brownian local times remain valid, mutatis mutandis, under the limiting laws of Brownian motion penalized by a function of its one-sided maximum.