The antithetic variates technique consists, for every sample path obtained, in taking its antithetic path - that is given a path \(\varepsilon_1,\dots,\varepsilon_M\) to also take, for example, \(-\varepsilon_1,\dots,-\varepsilon_M\) or \(1-\varepsilon_1,\dots,1-\varepsilon_M\).
The common random numbers is a variance reduction technique to apply when we are comparing two random systems, e.g., \(E(f(X_1) - g(X_2))\).
Control variates method is a variance reduction technique that exploits information about the errors in estimates of known quantities to reduce the error of an estimate of an unknown quantity.
Importance sampling is a general technique for estimating properties of a particular distribution, while only having samples generated from a different distribution rather than the distribution of interest.
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