Convergence of numerical time-averaging and stationary measures via Poisson equations
Repository Usage Stats
Numerical approximation of the long time behavior of a stochastic di.erential 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 schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
Published Version (Please cite this version)10.1137/090770527
Publication InfoMattingly, Jonathan Christopher; Stuart, AM; & Tretyakov, MV (2010). Convergence of numerical time-averaging and stationary measures via Poisson equations. SIAM Journal on Numerical Analysis, 48(2). pp. 552-577. 10.1137/090770527. Retrieved from http://hdl.handle.net/10161/15777.
This is constructed from limited available data and may be imprecise. To cite this article, please review & use the official citation provided by the journal.
More InfoShow full item record
Professor of Mathematics
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and