Discrimination with respect to a Gaussian process (Q2266522)

Let \((N_ t)\) and \((Y_ t)\), t in [0,1], be stochastic processes on (\(\Omega\),\({\mathcal B},P)\). Supppose that \((N_ t)\) is Gaussian, m.s. continuous, zero mean, and vanishes a.s. at \(t=0\). Let \(\nu_ Y\) and \(\nu_ N\) be the induced measures on \({\mathbb{R}}^{[0,1]}\). Conditions are obtained for \(\nu_ Y\) to be absolutely continuous w.r.t. \(\nu_ N\). Expressions for the Radon-Nikodym derivative are derived. Further results on these problems are obtained for measures induced on \(L_ 2[0,1]\) and on C[0,1].