References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Convergence rates for adaptive weak approximation of stochastic differential equationsPrimeFaces.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});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2005 (English)In: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 23, no 3, 511-558 p.Article in journal (Refereed) Published
##### Abstract [en]

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

2005. Vol. 23, no 3, 511-558 p.
##### Keyword [en]

adaptive mesh refinement algorithm, almost sure convergence, computational complexity, Monte Carlo method, stochastic differential equations, finite-element methods, error
##### National Category

Computational Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-14798DOI: 10.1081/sap-200056678ISI: 000229613900005ScopusID: 2-s2.0-20444378209OAI: oai:DiVA.org:kth-14798DiVA: diva2:332839
#####

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##### Note

QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2010-08-25Bibliographically approved
##### In thesis

Convergence rates of adaptive algorithms for weak approximations of Ito stochastic differential equations are proved for the Monte Carlo Euler method. Two algorithms based either oil optimal stochastic time steps or optimal deterministic time steps are studied. The analysis of their computational complexity combines the error expansions with a posteriori leading order term introduced in Szepessy et al. [Szepessy, A.. R. Tempone, and G. Zouraris. 2001. Comm. Pare Appl. Math. 54:1169-1214] and ail extension of the convergence results for adaptive algorithms approximating deterministic ordinary differential equations, derived in Moon et al. [Moon, K.-S., A. Szepessy, R. Tempone, and G. Zouraris. 2003. Numer. Malh. 93:99-129]. The main step in the extension is the proof of the almost sure convergence of the error density. Both adaptive alogrithms are proven to stop with asymptotically optimal number of steps up to a problem independent factor defined in the algorithm. Numerical examples illustrate the behavior of the adaptive algorithms, motivating when stochastic and deterministic adaptive time steps are more efficient than constant time steps and when adaptive stochastic steps are more efficient than adaptive deterministic steps.

1. Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations$(function(){PrimeFaces.cw("OverlayPanel","overlay9210",{id:"formSmash:j_idt731:0:j_idt735",widgetVar:"overlay9210",target:"formSmash:j_idt731:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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