Convergence rate of weak Local Linearization schemes for stochastic differential equations with additive noise

There exists a diversity of weak Local Linearization (LL) schemes for the integration of stochastic differential equations with additive noise, which differ in the algorithms employed for the numerical implementation of the weak Local Linear discretizations. Despite convergence results for these discretizations have been already developed, the convergence of the weak LL schemes has not been considered up to date. In this work, a general result concerning the convergence rate of the weak LL schemes is presented, as well as specificities for a number of particular schemes. As an application, the convergence of weak LL schemes for equations driven by Poisson processes is presented in addition.