Cameron-Martin theorem
= Cameron-Martin theorem
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{wiki}
Translation of <Wiener measure> by a path $h$ is equivalent to Wiener measure exactly when $h$ belongs to the <Cameron-Martin space of Wiener measure>. In that case the density is
$$
\exp\left(\int_0^Th'(s)\,dB_s-\frac12\int_0^T|h'(s)|^2ds\right).
$$
Translation by any continuous path outside that space produces a singular measure.