Martedì 30 Giugno 2015, alle ore 15 precise il Prof. Abdul-Lateef Haji-Ali (King Abdullah University of Science and Technology)
presso la sala conferenze dell'IMATI-CNR di Pavia, terrà un seminario dal titolo:
MULTI-INDEX MONTE CARLO: WHEN SPARSITY MEETS SAMPLING
nell'ambito del Seminario di Matematica Applicata (IMATI-CNR e Dipartimento di Matematica, Pavia).
Al termine della conferenza sarà organizzato un piccolo rinfresco.
We propose and analyze a novel Multi-Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the Multilevel Monte Carlo (MLMC) method first described by Heinrich and Giles. Inspired by Giles's seminal work, we use in MIMC high-order mixed differences instead of using first-order differences as in MLMC to reduce the variance of the hierarchical differences dramatically. This in turn yields new and improved complexity results, which are natural generalizations of Giles's MLMC analysis and which increase the domain of the problem parameters for which we achieve the optimal convergence. Moreover, in MIMC, the rate of increase of required memory with respect to TOL is independent of the number of directions up to a logarithmic term which allows far more accurate solutions to be calculated for higher dimensions than what is possible when using MLMC.
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