Numerical invariant measure for periodic stochastic differential equations with superlinear terms

This work studies the invariant measure of numerical approximation to a class of superlinear stochastic differential equations (SDEs) with periodic coefficients by the truncated Euler–Maruyama (EM) method. The existing studies on numerical invariant measures mostly focus on autonomous SDEs. To the best of our knowledge, this paper is the first devoted to the case of non-autonomous SDEs which allow superlinear growth. Technical challenges including superlinearity, periodicity and time-inhomogeneity of the system make this a non-trivial work. Not only the existence and uniqueness of a numerical invariant measure but also the convergence of the numerical invariant measure to the underlying one are deduced in the Wasserstein metric. Consequently, a case study is carried out to demonstrate the main results.