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 ...

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process “the invelope” and show that it is an almost surely uniquely defined function of integrated Brownian motion. Its role is comparable to the role of the...

A fundamental result of Biane (1998) states that a process with freely independent increments has the Markov property, but that there are two kinds of free Lévy processes: the first kind has stationary increments, while the second kind has stationary transition operators. We show that a process of the first kind (with mean zero and finite variance) has the same transition operators as the free ...

A process associated with integrated Brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities, respectively. We call this process \the invelope" and show that it is an almost surely uniquely de ned function of integrated Brownian motion. Its role is comparable to the role of the ...

An elementary approach is used to derive a Bayes-type formula, extending the Kallianpur–Striebel formula for the nonlinear filters associated with the Gaussian noise processes. In the particular cases of certain Gaussian processes, recent results of Kunita and of Le Breton on fractional Brownian motion are derived. We also use the classical approximation of the Brownian motion by the Ornstein–U...

Abstract. Let X be a Lévy process in R, dU3, obtained by subordinating Brownian motion with a subordinator with a positive drift. Such a process has the same law as the sum of an independent Brownian motion and a Lévy process with no continuous component. We study the asymptotic behavior of the Green function of X near zero. Under the assumption that the Laplace exponent of the subordinator is ...

In this study, the Brownian motion and thermophoresis effects on the MHD ferrofluid flow over a cone with thermal radiation were discussed. Kerosene with the magnetic nanoparticles (Fe3O4) was considered. A set of transformed governing nonlinear coupled ordinary differential equations were solved numerically using Runge-Kutta based shooting technique. A simulation was performed by mixing ferrou...

A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M ≫ 1 and the gas is represented by just one point particle of mass m = 1, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of...

Let D be the Wiener sausage of width ε around two-sided Brownian motion. The components of 2-dimensional reflected Brownian motion in D converge to 1-dimensional Brownian motion and iterated Brownian motion, resp., as ε goes to 0.

Let D be the Wiener sausage of width " around two-sided Brownian motion. The components of 2-dimensional reeected Brownian motion in D converge to 1-dimensional Brownian motion and iterated Brownian motion, resp., as " goes to 0.