Randomized Quasi‐Monte Carlo

Abstract

Monte Carlo (MC) methods use independent uniform random numbers to sample realizations of random variables and sample paths of stochastic processes, often to estimate high‐dimensional integrals that can represent mathematical expectations. Randomized quasi‐Monte Carlo (RQMC) methods replace the independent random numbers by dependent uniform random numbers that cover the space more evenly. When estimating an integral, they can provide unbiased estimators whose variance converges at a faster rate than with Monte Carlo. RQMC can also be effective for the simulation of Markov chains, to approximate or optimize functions, to solve partial differential equations, for density estimation, and so on.