ON THE ABSOLUTE CONTINUITY OF MEASURES CORRESPONDING TO PROCESSES OF DIFFUSION TYPE RELATIVE TO A WIENER MEASURE
R Š Lipcer, A N Širjaev · Mathematics of the USSR-Izvestiya · 1972
In this work there are given necessary and sufficient conditions for the absolute continuity and equivalence , , of a Wiener measure and a measure corresponding to a process of diffusion type with differential .The densities (the Radon-Nikodým derivatives) of one measure with respect to the other are found. Questions of the absolute continuity and equivalence of measures and are investigated for the case when is an Ito process. Conditions under which an Ito process is of diffusion type are derived. It is proved that (up to equivalence) every process for which is a process of diffusion type.