--- res: bibo_abstract: - In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14, 1477–1500 (doi:10.4310/CMS.2016.v14. n6.a1)), it has been established that, for every arbitrarily slow convergence speed and every natural number d ? {4, 5, . . .}, there exist d-dimensional stochastic differential equations with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence. In this paper, we strengthen the above result by proving that this slow convergence phenomenon also arises in two (d = 2) and three (d = 3) space dimensions.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Mate foaf_name: Gerencser, Mate foaf_surname: Gerencser foaf_workInfoHomepage: http://www.librecat.org/personId=44ECEDF2-F248-11E8-B48F-1D18A9856A87 - foaf_Person: foaf_givenName: Arnulf foaf_name: Jentzen, Arnulf foaf_surname: Jentzen - foaf_Person: foaf_givenName: Diyora foaf_name: Salimova, Diyora foaf_surname: Salimova bibo_doi: 10.1098/rspa.2017.0104 bibo_issue: '2207' bibo_volume: 473 dct_date: 2017^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/13645021 dct_language: eng dct_publisher: Royal Society of London@ dct_title: On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions@ ...