Convergence of numerical time-averaging and stationary measures via poisson equations
Mattingly, Jonathan C., Stuart, A. M. and Tretyakov, M. V.. (2010) Convergence of numerical time-averaging and stationary measures via poisson equations. SIAM Journal on Numerical Analysis, Vol.48 (No.2). pp. 552-577. ISSN 0036-1429Full text not available from this repository.
Official URL: http://dx.doi.org/10.1137/090770527
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 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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||SIAM Journal on Numerical Analysis|
|Publisher:||Society for Industrial and Applied Mathematics|
|Number of Pages:||26|
|Page Range:||pp. 552-577|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||National Science Foundation (U.S.) (NSF), Sloan Fellowship, Engineering and Physical Sciences Research Council (EPSRC), ERC|
|Grant number:||DMS-0616710, DMS-0449910, EP/D049792/1|
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