Abstract
An interesting way to compare the biased random number technique to more conventional biasing techniques is to consider what is really calculated by analog Monte-Carlo. Each history is associated with a random number sequence \(\vec r_i\) and a history score \(T(\vec r_i )\) that depends on the random walk specified by \(\vec r_i\). The random number sequence \(\vec r_i\) is selected from a uniform density \(f(\vec r)\) of random number sequences. The expected score is then: $$E = \smallint T(\vec r)f(\vec r)d\vec r$$ .
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