CHARACTERIZATION OF FRACTIONAL BROWNIAN MOTIONS WITH APPLICATIONS TO SIGNAL DETECTION.

Summary form only given, as follows. The authors consider the problem of detecting a (possibly stochastic) signal S(t) corrupted by a fraction Gaussian noise process W//H (t) having a spectral density proportional to f**1- **2 **H, 1/2 less than equivalent to H less than 1. It can be shown that such a noise process can be regarded as the derivative of fractional Brownian motion B//H (t) with self-similarity parameter H. This leads the authors to consider the observation model dY(t) equals s(t)dt plus DB//H (t). They utilize a representation of the process B//H (t) which leads naturally to a characterization of the reproducing-kernel Hilber space of the process as well as an interesting 'pre-whitening' result. This allows them to draw some conclusions concerning singularity and equivalence of the detection problem as well as the design of optimum detectors.