Consider the center of mass of a supercritical branching-Brownian motion, or that of a supercritical super-Brownian motion. In this paper we prove that it is a Brownian motion being slowed down such that it tends to a limiting position almost surely, which, in a sense complements a result of Tribe on the final behavior of a critical super-Brownian motion. This is shown to be true also for a mod...

Fundamental to many applications in financial engineering is the normal (Gaussian) distribution. It is the building block for simulating such basic stochastic processes as Brownian motion and geometric Brownian motion. In this section, we will go over algorithms for generating univariate normal rvs and learn how to use such algorithms for constructing sample paths of Brownian motion and geometr...

Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...

This paper seeks to study standard Brownian motion and some of its properties. We construct this stochastic process and demonstrate a few properties including continuity and non-differentiability.

We show that Brownian motion on any unbounded submanifold P in an ambient manifold N with a pole p is transient if the following conditions are satisfied: The p-radial mean curvatures of P are sufficiently small outside a compact set and the p-radial sectional curvatures of N are sufficiently negative. The ‘sufficiency’ conditions are obtained via comparison with explicit transience criteria fo...

We survey some new progress on the pricing models driven by fractional Brownian motion or mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with transaction costs. We end the paper by giving some approximation results and indicating...

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the importa...

in this paper, unsteady two phase simulation of nanofluid flow and heat transfer between moving parallel plates, in presence of the magnetic field is studied. the significant effects of thermophoresis and brownian motion have been contained in the model of nanofluid flow. the three governing equations are solved simultaneously via galerkin method. comparison with other works indicates that this...

Asset prices are typically modeled with the geometric Brownian motion (GBM). Correlation between the assets is exogenously modeled and then ad-hoc assigned to the asset prices. This is conceptually and mathematically unsatisfying. We create a new, simple approach, which simultaneously models stochastic volatility and stochastic correlation. This approach replicates the realworld volatility – co...

Brownian-Laplace motion is a Lévy process which has both continuous (Brownian) and discontinuous (Laplace motion) components. The increments of the process follow a generalized normal Laplace (GNL) distribution which exhibits positive kurtosis and can be either symmetrical or exhibit skewness. The degree of kurtosis in the increments increases as the time between observations decreases. This an...