Suppose that the intensity of the Poisson process \(N\) is equal to 1 and let \(d L_{t}=L_{t^{-}} \gamma_{t} d M_{t}, L_{0}=1\) where \(\gamma\) is a non-deterministic \(\mathbf{F}^{W}\)-predictable process. Denote by \(\mathbb{Q}^{\gamma}\) the probability \(\left.\mathbb{Q}^{\gamma}\right|_{\mathcal{F}_{t}}=\left.L_{t} \mathbb{P}\right|_{\mathcal{F}_{t}}\). The filtration of \(M^{\gamma}\) is that of both \(M\) and \(\int_{0}^{t} \gamma_{s} d s\), hence, the processes \(W\) and \(M^{\gamma}\) are not independent.