Chhikara and Folks (1988) show that the inverse gaussian distribution arises as the first passage time for a wiener process. However, there are several steps I don't quite understand. In particular, some of the steps, e.g. the last one on p. 26, in finding the Laplace transform $f^*$, are rather opaque.
Are there other places where this derivation is shown? Google yields nothing so far.