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1) Antithetical sampling reduces the variance in that for each path generated by random numbers in the interval [0,1] (representing probabilities), it generates another path that is correlated to that path (for example by taking the 1 - random number from the first path). As such, by construction, it forces there to be another correlated path in the ...


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Take your equation, $ dr(t) = \left(\eta - \gamma r(t) \right)dt + c \, dX(t)$ and rearrange it as you suggested: $dr(t) = \gamma \left(\frac{\eta}{\gamma} - r(t) \right)dt + c \, dX(t)$ $dr(t) = \gamma \left(s - r(t) \right)dt + c \, dX(t)$ Now if you multiply through by the integrating factor $e^{\gamma t}$ as you mentioned, you should get this ...


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