Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme

We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class parabolic semilinear stochastic partial differential equations driven by additive noise, under one-sided Lipschitz continuity condition. The setting encompasses nonlinearities with polynomial growth. First, we prove that moment bounds for numerical hold, at most dependence respect time horizon. Second, apply this result obtain error estimates, in weak sense, terms time-step size and horizon, quantify approximate averages invariant distribution continuous-time process. justify efficiency using distribution, since computational cost does not suffer from growth bounds. To best our knowledge, is first literature concerning approximation SPDEs non-globally coefficients scheme.