Adaptive weak approximation of diffusions with jumps
2008 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 46, no 4, 1732-1768 p.Article in journal (Refereed) Published
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational error, with computable leading order term in a posteriori form, based on stochastic flows and discrete dual backward problems which extends the results in [STZ]. These expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or quasi-deterministic time steps are described. Numerical examples show the performance of the proposed error approximation and of the described adaptive time-stepping methods.
Place, publisher, year, edition, pages
2008. Vol. 46, no 4, 1732-1768 p.
diffusions with jumps, weak approximation, error control, Euler-Maruyama method, a posteriori error estimates, backward dual functions
IdentifiersURN: urn:nbn:se:kth:diva-55331DOI: 10.1137/060669632ISI: 000256453400004ScopusID: 2-s2.0-55349117825OAI: oai:DiVA.org:kth-55331DiVA: diva2:471467
QC 201201032012-01-022012-01-022012-04-14Bibliographically approved