Weak Versions of Stochastic Adams-Bashforth and Semi-implicit Leapfrog Schemes for SDEs

We consider the weak analogues of certain strong stochastic numerical schemes considered in [10], namely a Adams-Bashforth scheme and a semi-implicit leapfrog scheme. We show that the weak version of the Adams-Bashforth scheme converges weakly with order 2, and the weak version of the semi-implicit leapfrog scheme converges weakly with order 1. We also note that the weak schemes are computationally simpler and easier to implement than the corresponding strong schemes, resulting in savings in both programming and computational effort.