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Adaptive Monte Carlo Algorithms for Stopped DiffusionPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true}); PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt197",{id:"formSmash:j_idt197",widgetVar:"widget_formSmash_j_idt197",onLabel:"Hide others and affiliations",offLabel:"Show others and affiliations"});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2005 (English)In: Multiscale Methods in Science and Engineering, Berlin: Springer-Verlag , 2005, 44, 59-88 p.Chapter in book (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Berlin: Springer-Verlag , 2005, 44. 59-88 p.
##### Series

, Lecture Notes in Computational Science and Engineering, ISSN 1439-7358 ; 44
##### Keyword [en]

adaptive mesh refinement algorithm, diffusion with boundary, barrier option, Monte Carlo method, weak approximation
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-7419DOI: 10.1007/3-540-26444-2_3ScopusID: 2-s2.0-84880255490ISBN: 978-3-540-26444-6OAI: oai:DiVA.org:kth-7419DiVA: diva2:12442
#####

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##### Note

QC 20100824Available from: 2007-08-31 Created: 2007-08-31 Last updated: 2010-08-24Bibliographically approved
##### In thesis

We present adaptive algorithms for weak approximation of stopped diffusion using the Monte Carlo Euler method. The goal is to compute an expected value of a given function *g* depending on the solution *X* of an Itô stochastic differential equation and on the first exit time τ from a given domain.

The main steps in the extension to stopped diffusion processes are to use a conditional probability to estimate the first exit time error and introduce difference quotients to approximate the initial data of the dual solutions.

1. Adaptivity for Stochastic and Partial Differential Equations with Applications to Phase Transformations$(function(){PrimeFaces.cw("OverlayPanel","overlay12445",{id:"formSmash:j_idt731:0:j_idt735",widgetVar:"overlay12445",target:"formSmash:j_idt731:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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