Modified Monte Carlo Methods Using Quasi-Random Sequences
Computational experiments have shown that Monte Carlo methods using quasi-random sequences lose some of their effectiveness for integration problems in which the dimension is large or the integrand is not smooth. In this paper, two modified Monte Carlo methods are developed, which regain an enhanced convergence rate. The standard rejection method involves discontinuities, corresponding to the decision to accept or reject. In place of this, a smoothed rejection method is formulated and found to be very effective when used with quasi-random sequences. Monte Carlo evaluation of Feynman-Kac path integrals involves high dimension, one dimension for each discrete time interval. Through an alternative discretization, the effective dimension of the integration domain is drastically reduced, so that quasi-random sequences are effective.
KeywordsImportance Sampling Effective Dimension Monte Carlo Estimate Monte Carlo Integration Importance Function
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