Is the Driving Force of a Continuous Process a Brownian Motion or Fractional Brownian Motion?

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

CFD simulations on natural convection heat transfer of alumina-water nanofluid with Brownian motion effect in a 3-D enclosure

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 ...

Investigation of Brownian Motion of CuO-Water Nanofluid in a Porous Cavity with Internal Heat Generation by Using of LTNE Model

In this paper, the effect of the Brownian term in natural convection of CuO-Water nanofluid inside a partially filled porous cavity, with internal heat generation has been studied. It is assumed that the viscosity and thermal conductivity of nanofluid consists of a static part and a Brownian part of which is a function of temperature and the volume fraction of nanofluid. Because of internal hea...

Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion

The problem of optimal ltering is investigated in a continuous time linear Gaussian system where the signal is a xed random variable and the noise driving the observation process is a fractional Brownian motion with Hurst parameter H 2 (1=2; 1). Closed form expressions are derived both for the optimal lter and the variance of the ltering error. Then an application to the determination of the be...