On an application of infinitely divisible distributions to quadrature problems (Q908678)

Mean square errors are computed for approximation by the rectangular and Monte Carlo methods to integrals on [0,1] of continuous functions contained in a stochastic process generated by an infinitely divisible distribution. The error for the rectangular approximation with N equal partitions is \(O(1/N^ 2)\) and for the Monte Carlo approximation with N terms it is O(1/N). The Wiener process and the process generated by the Poisson distribution are examples of processes which are included in the theory.