Absolute continuity of measures in the class of Markov and semi-Markov processes of diffusion type (Q5907037)

Let \(\{P_x^{(i)}\), \(x\in\mathbb{R}^1\}\), \(i=1,2\), be families of measures, corresponding to two one-dimensional semi-Markov processes of diffusion type. Conditions are found for local absolute continuity of \(P_x^{(2)}\) with respect to \(P_x^{(1)}\). An explicit formula for the related density function is also derived.