ABSTRACT
Absolute continuity and singularity of measures induced by stochastic processes are a classical problem of stochastic process theory. Semimartingale theory and stochastic calculus provide a completely new approach to it. This chapter introduces the basic tools—Hellinger processes and discusses absolute continuity and singularity of measures. It also discusses generalizations of absolute continuity and singularity—contiguity and entire separation of measures, and the associated problem of convergence in variation of measures and presents application to Levy process. It starts to discuss the absolute continuity and singularity of measures under the assumptions.
