The self-organization of particles in a two-phase system in the coexistence region through a diffusive mechanism is known as Ostwald ripening. A mesoscopic model derived from the spin exchange Ising model is used here in a computational study of Ostwald ripening. The typical cluster size is...

A numerical method for a class of Itô stochastic differential equations with a finite delay term is introduced. The method is based on the forward Euler approximation and is parameterised by its time step. Weak convergence with respect to a class of smooth test functionals is established by...

A numerical method for a class of Itô stochastic differential equations with a finite delay term is introduced. The method is based on the forward Euler approximation and is parameterised by its time step. Weak convergence with respect to a class of smooth test functionals is established by...

We consider a general nonlinear diffusion, typified by those deriving from Fitzhugh–Nagumo or Hindmarsh–Rose models of nerve-cell dynamics, perturbed also by 2-parameter white noise. In order to investigate the effects of the nonlinearity, we find for general boundary conditions the mean to...

This note analyzes the mean-reverting behavior of time-homogeneous Heath-Jarrow-Morton (HJM) forward rate models in the weighted Sobolev spaces {H<Subscript> w </Subscript>}<Subscript> w </Subscript>. An explicit sufficient condition is given under which invariant measures exist for the HJM dynamics. In particular, every HJM model with...</subscript></subscript>

In this article the forward rates equation of the Musiela model is analysed. The equation is studied in the Sobolev spaces $H^1_\gamma({\Bbb R}^+)$ and $H^1({\Bbb R}^+)$. Explicit mild solutions and equivalent conditions for the existence and uniqueness of invariant measures are presented.