On the correct discrimination of Gaussian hypotheses (Q2567789)

Let \(\gamma_0\) and \(\gamma_1\) be two centered equivalent Gaussian measures on a linear space. The distinction problem of these measures is said to be correct provided there exists a Hilbert space \(H\) which is the linear support of \(\gamma_0\) as well as \(\gamma_1\) and the Radon-Nikodym derivative \(d\gamma_0/d\gamma_1\) has a version which is continuous with respect to the norm of \(H\). The author presents a condition under which this problem is correct and a condition under which it is not correct. For more general results see the author [Zap. Nauchn. Semin. POMI 320, 129-149 (2004; Zbl 1136.60303)].