CONTROLLING CORRELATIONS IN PARALLEL MONTE-CARLO

Effects and detection of correlations in parallel Monte Carlo are discussed, on the assumption that each processor uses a sequence of truly random numbers, but the sequences are mutually correlated. Depending on the parallel implementation of the algorithm, effects may concern the mean value of the solution or only its variance. In the first case an alternative implementation of the algorithm is suggested. In the second - where it is possible to lose control of the result's accuracy - a control estimator is introduced which ensures correct computation of the variance. In this way one obtains reliability even when coprocessors are not independent. The same estimator, moreover, monitors the correlation transmitted from the source of random numbers to the results, i.e. the effect on computation velocity. Numerical examples show the sensitivity of the implemented control.