An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems

Abstract We develop an adaptive algorithm for large SDE systems, which automatically selects (quasi-)deterministic time steps the semi-implicit Euler method, based on a posteriori weak error estimate. Main tools to construct estimator are representation of approximation via Kolmogorov’s backward equation, priori bounds its solution and Clark–Ocone formula. For certain class we validate optimal convergence order 1 estimator, termination method it within $${{\mathcal {O}}}(\mathtt{Tol}^{-1})$$ O ( Tol - 1 ) steps.