Comparison of two procedures for global stochastic estimation of functions

Numerical stochastic procedures for estimating integrals depending on parameter are considered. The discrete mesh on the domain of definition of parameter is introduced, and the Monte Carlo algorithms for estimating integral in mesh points are used. The independent Monte Carlo estimates and the "depended tests" method are compared. It is proved that the "depended tests" method is "better" in the sense of error asymptotics, but in some special cases (corresponding numerical examples are given) the computational cost for independent estimates may be less.