ABSTRACT
In this paper the role of the evolution operator family in the analysis of (higher order) stochastic differential equations and in the theory of likelihood ratios in stochastic processes is studied. Although the existence and unicity of solutions of SDEs can be established with methods of semi-group theory, further work including the sample path properties of solutions demand a (full) use of evolution families. Moreover, in inference theories of stochastic processes, involving testing composite hypotheses, a detailed study of evolution families is indispensable. Some related and several new problems arising in these studies are included.
