Publications [#164683] of Jonathan C. Mattingly

Papers Submitted

1. with Andrew M. Stuart and M.V. Tretyakov, Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations (2009) [0908.4450v2]
   (last updated on 2009/10/26)

   Abstract:
   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 advantage of this approach is its simplicity and universality. It works equally well for a range of explicit and implicit schemes including those with simple simulation of random variables, and for general hypoelliptic SDEs. An analogy between this approach and Stein's method is indicated. Some practical implications of the results are discussed.