Multilevel Richardson-Romberg extrapolation
The paper proposes to improve the standard multilevel Monte Carlo (MLMC) paradigm by combining the MLMC estimator and the multistep Richardson-Romberg extrapolation with a general parametrized framework to formalize the optimization of a biased Monte Carlo simulation based on the \(L^{2}\)-error minimization. As examples of applications, a weak expansion of the error at any order is established for the time discretization of stochastic processes and the nested Monte Carlo method. Some numerical experimental results are presented.
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