%0 Journal Article %T Strong convergence of some drift implicit Euler scheme. Application to the CIR process. %+ Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) %+ Mathematical Risk handling (MATHRISK) %A Alfonsi, Aurélien %< avec comité de lecture %@ 0167-7152 %J Statistics and Probability Letters %I Elsevier %V 83 %N 2 %P 602-607 %8 2013 %D 2013 %Z 1206.3855 %R 10.1016/j.spl.2012.10.034 %K Discretization scheme %K Cox-Ingersoll-Ross model %K Strong error %K Lamperti transformation. %K Lamperti transformation %Z Mathematics [math]/Probability [math.PR]Journal articles %X We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order 1. In the CIR case, Dereich, Neuenkirch and Szpruch have shown recently a strong convergence of order 1/2 for this scheme. Here, we obtain a strong convergence of order 1 under more restrictive assumptions on the CIR parameters. %G English %2 https://enpc.hal.science/hal-00709202/document %2 https://enpc.hal.science/hal-00709202/file/drift_implicit.pdf %L hal-00709202 %U https://enpc.hal.science/hal-00709202 %~ ENPC %~ INRIA %~ INRIA-ROCQ %~ CERMICS %~ INSMI %~ PARISTECH %~ INRIA_TEST %~ TESTALAIN1 %~ INRIA2 %~ UNIV-EIFFEL %~ UPEM-UNIVEIFFEL