Langevin equations with multiplicative noise: Application to domain growth

Langevin Equations of Ginzburg-Landau form, with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hiliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical predictions of the linear analysis. We also present simulation results for spinodal decomposition at large times.

Anticipating linear stochastic differential equations driven by a Lévy process

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformations on Wiener space and developped by Buckdahn [7] to the canonical Lévy space, which is introduced in [25].