On the detection problem (Corresp.)

The detection problem for the model "signal-plus-noise," where the "noise" is represented by a Wiener process, has been approached primarily through the use of martingale theory. There are two core results: a new version of what is called "Girsanov's theorem" and the fact that the Wiener measure on the space of continuous functions can be generated by any Wiener process. In this correspondence a new version of "Girsanov's theorem" is derived and some fragmentary results concerning the measures associated with martingales are presented.