Adaptive stratified Monte Carlo algorithm for numerical computation of integrals

In this paper, we aim to compute numerical approximations of the integral of a function by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called indicators which indicate where the variance takes relative large values. The stratification method is based on the optimal allocation strategy in order to decrease the variance from one iteration to another. Numerical experiments show and confirm the efficiency of our algorithm. (C) 2018 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.Y. All rights reserved.