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We show a Cameron-Martin theorem for Slepian processes$W_t:=\frac{1}{\sqrt{p}}(B_t-B_{t-p}), t\in [p,1]$, where $p\geq \frac{1}{2}$and $B_s$ is Brownian motion. More exactly, we determine the class of functions$F$ for which a density of $F(t)+W_t$ with respect to $W_t$ exists. Moreover,we prove an explicit formula for this density. p-Slepian processes are closelyrelated to Slepian processes. p-Slepian processes play a prominent role amongothers in scan statistics and in testing for parameter constancy when data aretaken from a moving window.

The Cameron-Martin Theorem for (p-)Slepian processes