Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations

@article{Mattingly2010ConvergenceON,
  title={Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations},
  author={Jonathan C. Mattingly and Andrew M. Stuart and Michael V. Tretyakov},
  journal={SIAM J. Numer. Anal.},
  year={2010},
  volume={48},
  pages={552-577}
}
Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit… 
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