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Adaptive weak approximation of diffusions with jumps
Universidad de la República, Iguá 4225, Montevideo, Uruguay.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Div of Applied Math - Statistics, Univ of Crete. (Numerical Analysis)
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
Abstract [en]

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.
Keyword [en]
diffusions with jumps, weak approximation, error control, Euler-Maruyama method, a posteriori error estimates, backward dual functions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-55331DOI: 10.1137/060669632ISI: 000256453400004Scopus ID: 2-s2.0-55349117825OAI: oai:DiVA.org:kth-55331DiVA: diva2:471467
Note
QC 20120103Available from: 2012-01-02 Created: 2012-01-02 Last updated: 2017-12-08Bibliographically approved

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