We establish an invariance principle for the barycenter of a Brunet–Derrida particle system in d dimensions. The model consists N particles undergoing dyadic branching Brownian motion with rate 1. At event, number is kept equal to by removing located furthest away from barycenter. To prove principle, key step Harris recurrence process viewed its

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 this paper the effect of using various models for conductivity and viscosity considering brownian motion of nanoparticles is investigated. this study is numerically conducted inside a cavity full of water-al2o3 nanofluid at the case of mixed convection heat transfer. the effect of some parameters such as the nanoparticle volume fraction, rayleigh, richardson and reynolds numbers has been exa...

We present a swarm model of Brownian particles with harmonic interactions, where the individuals undergo canonical active Brownian motion, i.e., each Brownian particle can convert internal energy to mechanical energy of motion. We assume the existence of a single global internal energy of the system. Numerical simulations show amorphous swarming behavior as well as static configurations. Analyt...

We provide a method for the generation of paths of Lévy processes which has many of the benefits that the Brownian bridge construction has for Brownian motion. We show how, using our method, one can apply stratified sampling and quasi-Monte Carlo methods to obtain better numerical schemes analog to the Brownian case. As a numerical example we consider the problem of pricing an asian option in t...