Parareal method is a numerical method to solve time - evolutional problems in parallel, which uses two propagators: the coarse - fast and inaccurate - and the fine - slow but more accurate. Instead of running the fine propagator on the whole time interval, we divide the time space into small time intervals, where we can run the fine propagator in parallel to obtain the desired solution, with...

We study the Multi-level Monte Carlo method introduced by Giles [3] and its applications to finance which is significantly more efficient than the classical Monte Carlo method. This method for the stochastic differential equations driven by only Brownian Motion had been studied by Ben Alaya and Kebaier [2]. Here, we consider the stochastic differential equation driven by a pure jump Lévy...

We will review recent results on the propagation of waves on domains, with emphasis on two extreme cases: the exterior or the interior of a stricly convex domain. Understanding the wave localization, its amplitude and how it decays is fundamental for several (unrelated) problems and we will describe an interesting interplay between geometrical aspects and degenerate oscillatory integrals that...