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.