Central limit theorem for the multilevel Monte Carlo Euler method

Mohamed Ben Alaya (1) , Ahmed Kebaier (2) , Mohamed Ben Alaya (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 LAGA - Laboratoire Analyse, Géométrie et Applications

This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] which is significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central limit theorem of Lindeberg-Feller type for the multilevel Monte Carlo method associated with the Euler discretization scheme. To do so, we prove first a stable law convergence theorem, in the spirit of Jacod and Protter [Ann. Probab. 26 (1998) 267-307], for the Euler scheme error on two consecutive levels of the algorithm. This leads to an accurate description of the optimal choice of parameters and to an explicit characterization of the limiting variance in the central limit theorem of the algorithm. A complexity of the multilevel Monte Carlo algorithm is carried out.

Domains: Mathematics [math]; Probability [math.PR]

Mohamed Ben Alaya, Ahmed Kebaier, Mohamed Ben Alaya. Central limit theorem for the multilevel Monte Carlo Euler method. Annals of Applied Probability, 2015, 25 (1), pp.211-234. ⟨10.1214/13-AAP993⟩. ⟨hal-02332484⟩