PREDICTABLE CRITERIA FOR ABSOLUTE CONTINUITY AND SINGULARITY OF TWO PROBABILITY MEASURES
Friedrich Pukelsheim · Statistics & Risk Modeling · 1986
Predictable criteria for absolute continuity and singularity are established based on the multiplicative increments of the likelihood ratio process of the hypothesis relative to the alternative and not, as is usual, of the alternative relative to the hypothesis.This approach avoids any change of probability measures, disposes of an assumption on local absolute continuity, and allows for an arbitrary root of the like lihood ratio process rather than distinuguishing the square root case.