Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation∗

The pathwise error analysis of numerical schemes for SDE has been intensively studied [12, 21, 26, 30], whereas the weak error analysis started later with the work of Milstein [24,

In order to obtain an energy estimate without any condition on the time step ∆t, we choose a time discretization for the non-linear terms such that the right hand side of (3.4) is

Then we show the convergence of a sequence of discrete solutions obtained with more and more refined discretiza- tions, possibly up to the extraction of a subsequence, to a

Keywords : stochastic differential equation, Euler scheme, rate of convergence, Malliavin calculus.. AMS classification: 65C20 60H07 60H10 65G99

This has already been succesfully applied to the second order formula- tion of the acoustic wave equation and we focus here on the first order formulation of acoustic and

In our main result, we prove existence and uniqueness of the invariant distribution and exhibit some upper-bounds on the rate of convergence to equilibrium in terms of the

[1] Kazuo Aoki and Fran¸ cois Golse. On the speed of approach to equilibrium for a colli- sionless gas. On the distribution of free path lengths for the periodic Lorentz gas.

However, due to the lack of regularity of the space time white noise, equation (1.3) is not expected to possess a well defined solution in this case, and we therefore consider in