  There exists a diversity of weak Local Linearization (LL) schemes for the
integration of stochastic differential equations with additive noise, which
differ with respect to the algorithm that is employed in the numerical
implementation of the weak Local Linear discretizations. On the contrary to the
Local Linear discretization, the rate of convergence of the LL schemes has not
been considered up to now. In this work, a general theorem about this issue is
derived and further is applied to a number of specific schemes. As application,
the convergence rate of weak LL schemes for equations with jumps is also
presented.
