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Adaptive weak approximation of reflected and stopped diffusions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
2010 (English)In: Monte Carlo Methods and Applications, ISSN 1569-3961, Vol. 16, no 1, 1-67 p.Article in journal (Refereed) Published
Abstract [en]

We study the weak approximation problem of diusions, which are reflected at a subset of the boundary of a domain and stopped at the remaining boundary. First, we derive an error representation for the projected Euler method of Costantini, Pacchiarotti and Sartoretto [Costantini et al., SIAM J. Appl. Math., 58(1):73–102, 1998], based on which we introduce two new algorithms. The first one uses a correction term from the representation in order to obtain a higher order of convergence, but the computation of the correction term is, in general, not feasible in dimensions d> 1. The second algorithm is adaptive in the sense of Moon, Szepessy, Tempone and Zouraris [Moon et al., Stoch. Anal. Appl., 23:511–558, 2005], using stochastic refinement of the time grid based on a computable error expansion derived from the representation. Regarding the stopped diusion, it is based in the adaptive algorithm for purely stopped di usions presented in Dzougoutov, Moon, von Schwerin, Szepessy and Tempone [Dzougoutov et al., Lect. Notes Comput. Sci. Eng., 44, 59–88, 2005]. We give numerical examples underlining the theoretical results.

Place, publisher, year, edition, pages
2010. Vol. 16, no 1, 1-67 p.
National Category
URN: urn:nbn:se:kth:diva-55352DOI: 10.1515/MCMA.2010.001ScopusID: 2-s2.0-84858407403OAI: diva2:471519
Swedish e‐Science Research Center
QC 20120113Available from: 2012-01-02 Created: 2012-01-02 Last updated: 2012-05-24Bibliographically approved

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Bayer, ChristianSzepessy, Anders
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Mathematics (Dept.)Numerical Analysis, NA

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