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Convergence rates of adaptive algorithms for weak approximations of Itô stochastic differential equations are proved for the Monte Carlo Euler method. Two algorithms based either on 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 introduceddoi:10.1081/sap-200056678 fatcat:q42k2itkxzhmbeyjeqguhok7hy