# 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… CONTINUE READING

#### Topics from this paper.

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 102 CITATIONS

## Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme

VIEW 7 EXCERPTS

CITES BACKGROUND & METHODS

HIGHLY INFLUENCED

## Numerical Approximations to the Stationary Solutions of Stochastic Differential Equations

VIEW 1 EXCERPT

CITES METHODS

## Numerical analysis of highly oscillatory Stochastic PDEs

VIEW 2 EXCERPTS

CITES METHODS & BACKGROUND

### FILTER CITATIONS BY YEAR

### CITATION STATISTICS

**16**Highly Influenced Citations**Averaged 12 Citations**per year from 2018 through 2020

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 66 REFERENCES

## Computing ergodic limits for Langevin equations

VIEW 1 EXCERPT

## Stochastic numerics for mathematical physics

VIEW 2 EXCERPTS

## Exponential and Uniform Ergodicity of Markov Processes

VIEW 1 EXCERPT