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Update 4_Applications.md
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s-baumann committed Sep 15, 2020
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4 changes: 2 additions & 2 deletions docs/src/4_Applications.md
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Expand Up @@ -416,8 +416,8 @@ for any $\mu \in \Re^d$ where $d$ is the dimensionality of the function $G(\cdot

For each path $i = 1, ..., N$
* generate $Z_i \sim N(\mu, I)$
* $Y_i \leftarrow G(Z_i) \exp(-\mu^\prime Z_i + \frac{1}{2}\mu^\prime \mu)$
Then at the end return $\frac{\sum_{i=1}^N Y_i}{N}$
* calculate $Y_i \leftarrow G(Z_i) \exp(-\mu^\prime Z_i + \frac{1}{2}\mu^\prime \mu)$
return $\frac{\sum_{i=1}^N Y_i}{N}$

Now we need to figure out the vector $\mu$ which is composed of the shifts in the mean for each normal variable and thereby represents the change in probability measure. Note that for any vector our estimator should be unbiased and consistent but some can be more efficient than others. In the special case where $G(x) \geq 0 \forall x \in \Re^d$, an efficient choices is the vector $\mu$ which makes the following equation hold (for working out see equation 4.89 of Glasserman):

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