arXiv subjects
Publications and source records attributed to Andreas Gegg.
For $0 g(t) \; \text{for some } t\in[q,d]\right)$, $q< d\leq 2q$, in the case $g$ is a piecewise affine function. This formula can be used as approximation for the boundary crossing probability of an arbitrary boundary by approximating the boundary function by piecewise affine functions.
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 closely related to Slepian processes. p-Slepian processes play a prominent role among others in scan statistics and in testing for parameter constancy when data are taken from a moving window.