Sequences with low discrepancy generalisation and application to bobbins-monbo algorithm

Abstract

The use of uniform sequences with low discrepancy instead of random sequences in expectations computings is known to improve the rate of convergence. We propose and justify their use for the BOBBINS-MONRO algorithm. To this end we introduce the concepts of averaging and strong averaging systems and then we give under somewhat more re¬strictive assumptions than in the random case a convergence theorem and an estimation of the rate of convergence which show their superiority to random sequences