caa a22 4500 605497141 CHVBK 20210128100539.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10543-014-0511-3 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0511-3 A continuation multilevel Monte Carlo algorithm [Elektronische Daten] [Nathan Collier, Abdul-Lateef Haji-Ali, Fabio Nobile, Erik von Schwerin, Raúl Tempone] We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. The actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding variance and weak error. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients. Springer Science+Business Media Dordrecht, 2014 Multilevel Monte Carlo nationallicence Monte Carlo nationallicence Partial differential equations with random data nationallicence Stochastic differential equations nationallicence Bayesian inference nationallicence Collier Nathan Environmental Sciences Division, Oak Ridge National Lab, Climate Change Science Institute (CCSI), Oak Ridge, USA aut Haji-Ali Abdul-Lateef Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia aut Nobile Fabio MATHICSE-CSQI, EPF de Lausanne, Lausanne, Switzerland aut von Schwerin Erik Department of Mathematics, Kungliga Tekniska Högskolan, 100 44, Stockholm, Sweden aut Tempone Raúl Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia aut BIT Numerical Mathematics Springer Netherlands 55/2(2015-06-01), 399-432 0006-3835 55:2<399 2015 55 10543 https://doi.org/10.1007/s10543-014-0511-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0511-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Collier Nathan Environmental Sciences Division, Oak Ridge National Lab, Climate Change Science Institute (CCSI), Oak Ridge, USA aut NATIONALLICENCE 700 1- Haji-Ali Abdul-Lateef Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia aut NATIONALLICENCE 700 1- Nobile Fabio MATHICSE-CSQI, EPF de Lausanne, Lausanne, Switzerland aut NATIONALLICENCE 700 1- von Schwerin Erik Department of Mathematics, Kungliga Tekniska Högskolan, 100 44, Stockholm, Sweden aut NATIONALLICENCE 700 1- Tempone Raúl Applied Mathematics and Computational Sciences, KAUST, Thuwal, Saudi Arabia aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/2(2015-06-01), 399-432 0006-3835 55:2<399 2015 55 10543