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...

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...

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H > 1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the c...

Let X be a (two-sided) fractional Brownian motion of Hurst parameter H ∈ (0, 1) and let Y be a standard Brownian motion independent of X. Fractional Brownian motion in Brownian motion time (of index H), recently studied in [17], is by definition the process Z = X ◦ Y . It is a continuous, non-Gaussian process with stationary increments, which is selfsimilar of index H/2. The main result of the ...

In 2005, Nualart and Peccati [12] showed the so-called Fourth Moment Theorem asserting that, for a sequence of normalized multiple Wiener-Itô integrals to converge to the standard Gaussian law, it is necessary and sufficient that its fourth moment tends to 3. A few years later, Kemp et al. [8] extended this theorem to a sequence of normalized multiple Wigner integrals, in the context of the fre...

We present functional versions of recent results on the univariate distributions of the process Vx ,u = x +Wuτ(x), 0 ≤ u ≤ 1, where W• is the standard Brownian motion process, x > 0 and τ(x) = inf{t > 0 : Wt =−x}. Let {Wt}t≥0 be the standard univariate Brownian motion process and, for x > 0, Wx ,t := x +Wt , t ≥ 0, τ(x) := inf{t > 0 : Wx ,t = 0}. As is well known, τ(x) is a proper random variab...

in this paper, natural convection heat transfer over a vertical plate in a darcy porous medium saturated with a nanofluid subject to heat generation/absorption was theoretically studied. the governing partial differential equations were transformed to a set of ordinary differential equations using similarity transformations and solved using finite difference method. the influence of parametric ...

The detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the subspace spanned by linear functions. Karhunen–Loeve expansion for the process is obtained, together with the explicit formula for the Laplace transform of the squared L 2 norm. Distribution identities are established in connection with the second order Brownian bridge dev...

Given a standard Brownian motion B, we show that the equation Xt = x0 + Bt + β(Lt ) , t ≥ 0 , has a unique strong solution X. Here L is the symmetric local time of X at 0, and β is a given differentiable function with β(0) = 0, −1 < β′(·) < 1. (For linear β(·), the solution is the familiar skew Brownian motion).