# Dynamic splitting simulation

I have just spent so much time writing about this that I had better pause for a while and leave this as a placeholder.

## Splitting for static problems

We have a density $$f$$ on $$\bb R^d$$ and a quasi-monotone importance function $$S: \bb R^d\rightarrow\bb R.$$ We wish to simulate from a conditional

\begin{aligned} f^*(\vv x) &:=f(\vv x|S(\vv x)\geq\gamma)\\ &=\frac{1}{\ell(\gamma)}f(\vv x)\bb I\{S(\vv x)\geq\gamma)\} \end{aligned}

where $$\ell(\gamma)=\bb P[S(\vv X)\geq\gamma)],\quad \vv X \sim f.$$

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