Approximation by time discretization of special stochastic evolution equations.
Approximations of effective coefficients in stochastic homogenization
Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients
In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
Asymptotic behaviour of stochastic quasi dissipative systems
We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.
Asymptotic behaviour of stochastic quasi dissipative systems
We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.
Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations
This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial...