Adaptive weak approximation of stochastic differential equations
2001 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 54, no 10, 1169-1214 p.Article in journal (Refereed) Published
Adaptive time-stepping methods based on the Monte Carlo Euler method for weak approximation of Ito stochastic differential equations are developed. The main result is new expansions of the computational error, with computable leading-order term in a posteriori form, based on stochastic flows and discrete dual backward problems. The expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or deterministic time steps are described. Numerical examples illustrate when stochastic and deterministic adaptive time steps are superior to constant time steps and when adaptive stochastic steps are superior to adaptive deterministic steps. Stochastic time steps use Brownian bridges and require more work for a given number of time steps. Deterministic time steps may yield more time steps but require less work; for example, in the limit of vanishing error tolerance, the ratio of the computational error and its computable estimate tends to 1 with negligible additional work to determine the adaptive deterministic time steps.
Place, publisher, year, edition, pages
2001. Vol. 54, no 10, 1169-1214 p.
step-size control, global error
Engineering and Technology
IdentifiersURN: urn:nbn:se:kth:diva-20900ISI: 000170618900001OAI: oai:DiVA.org:kth-20900DiVA: diva2:339597
QC 201005252010-08-102010-08-102012-02-27Bibliographically approved