Adaptive weak approximation of reflected and stopped diffusions

Handle URI:
http://hdl.handle.net/10754/561620
Title:
Adaptive weak approximation of reflected and stopped diffusions
Authors:
Bayer, Christian; Szepessy, Anders; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
We study the weak approximation problem of diffusions, 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 diffusion, it is based in the adaptive algorithm for purely stopped diffusions 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. © de Gruyter 2010.
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Stochastic Numerics Research Group
Publisher:
Walter de Gruyter GmbH
Journal:
Monte Carlo Methods and Applications
Issue Date:
Jan-2010
DOI:
10.1515/MCMA.2010.001
Type:
Article
ISSN:
09299629
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBayer, Christianen
dc.contributor.authorSzepessy, Andersen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2015-08-03T09:00:26Zen
dc.date.available2015-08-03T09:00:26Zen
dc.date.issued2010-01en
dc.identifier.issn09299629en
dc.identifier.doi10.1515/MCMA.2010.001en
dc.identifier.urihttp://hdl.handle.net/10754/561620en
dc.description.abstractWe study the weak approximation problem of diffusions, 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 diffusion, it is based in the adaptive algorithm for purely stopped diffusions 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. © de Gruyter 2010.en
dc.publisherWalter de Gruyter GmbHen
dc.titleAdaptive weak approximation of reflected and stopped diffusionsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentStochastic Numerics Research Groupen
dc.identifier.journalMonte Carlo Methods and Applicationsen
dc.contributor.institutionInstitute for Mathematics, Royal Institute of Technology, S-10044 Stockholm, Swedenen
dc.contributor.institutionInstitute of Mathematics, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germanyen
kaust.authorTempone, Raulen
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