PREDICTABLE CRITERIA FOR ABSOLUTE CONTINUITY AND SINGULARITY OF TWO PROBABILITY MEASURES

Absolute Continuity and Singularity of Probability Measures in Functional Spaces

Is There a Predictable Criterion for Mutual Singularity of Two Probability Measures on a Filtered Space?

The theme of providing predictable criteria for absolute continuity and for mutual singularity of two density processes on a ltered probability space is extensively studied, e.g., in the monograph by J. Jacod and A. N. Shiryaev [JS]. While the issue of absolute continuity is settled there in full generality, for the issue of mutual singularity one technical di culty remained open ([JS], p210): ...

Absolute Continuity/Singularity and Relative Entropy Properties for Probability Measures Induced by Diffusions on Infinite Time Intervals

In this paper we study mutual absolute continuity, finiteness of relative entropy and the possibility of their equivalence for probability measures on C([0,∞);Rd) induced by diffusion processes. We also determine explicit events which distinguish between two mutually singular measures in certain one-dimensional cases.

Probability Structure Preserving and Absolute Continuity ✩

– The concept of probability structure preserving mapping is introduced. The idea is applied to define stochastic integral for fractional Brownian motion (fBm) and to obtain an anticipative Girsanov theorem for fBm.  2002 Éditions scientifiques et médicales Elsevier SAS AMS classification: 60H05; 60H07; 60H15; 60B11; 28B20

Absolute Continuity between the Wiener and Stationary Gaussian Measures

It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp [5] characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the spe...