Some stochastic control systems that are described by stochastic differential equations with a fractional Brownian motion are considered. The solutions of these systems are defined by weak solutions. These weak solutions are obtained by the transformation of the measure for a fractional Brownian motion by a Radon-Nikodym derivative. This weak solution approach is used to solve a control problem...

In [10] a “direct” stochastic transfer principle was introduced, which represented multiple integrals with respect to fractional Brownian motion in terms of multiple integrals with respect to standard Brownian motion. The method employed in [10] involved an operator Γ (n) H , mapping a class of functions LH to L 2. However, the operator does not map LH onto L 2. Hence Γ (n) H is not invertible....

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 ...

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H > 1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential eq...

This paper is concerned with various aspects of the Slepian process (Bt+1 −Bt, t ≥ 0) derived from one-dimensional standard Brownian motion (Bt, t ≥ 0). In particular, we offer an analysis of the local structure of the Slepian zero set {t : Bt+1 = Bt}, including a path decomposition of the Slepian process for 0 ≤ t ≤ 1. We also establish the existence of a random time T ≥ 0 such that the proces...

Let X be the fractional Brownian motion of any Hurst index H ∈ (0, 1) (resp. a semimartingale) and set α = H (resp. α = 12). If Y is a continuous process and if m is a positive integer, we study the existence of the limit, as ε→ 0, of the approximations Iε(Y,X) := {∫ t 0 Ys ( Xs+ε −Xs εα )m ds, t ≥ 0 } of m-order integral of Y with respect to X. For these two choices of X, we prove that the lim...

We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional : ( At := ∫ t 0 1Xs<0ds, t ≥ 0 ) . On the other hand, we describe FeynmanKac type penalisation results for long Brownian bridges thus completing some similar previous study for standard Brownian motion...

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.