Absolute continuity and singularity of two probability measures on a filtered space

Details Absolute continuity and singularity of two probability measures on a filtered space Absolute continuity and singularity of two probability measures on a filtered space

2008-02-04

arxiv.org/abs/0802.0385v4

Mathematics

Probability

18 pages, no figures

Scientific paper

Let $\mu$ and $\nu$ be fixed probability measures on a filtered space $(\Omega, {\cal F}, ({\cal F}_t)_{t\in {\bf R}^{+}})$. Denote by $\mu_T $ and $\nu_T $ (respectively, $\mu_{T-} $ and $\nu_{T-} $) the restrictions of the measures $\mu$ and $\nu$ on ${\cal F}_T $ (respectively, on ${\cal F}_{T-} $) for a stopping time $T$. We find the Hahn decomposition of $\mu_T $ and $\nu_T $ using the Hahn decomposition of the measures $\mu$, $\nu$, and the Hellinger process $h_t$ in the strict sense of order 1/2. The norm of the absolutely continuous component of $\mu_{T-} $ with respect to $\nu_{T-} $ is computed in terms of density processes and Hellinger integrals.

Affiliated with

Also associated with

No associations

Rating

Absolute continuity and singularity of two probability measures on a filtered space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Absolute continuity and singularity of two probability measures on a filtered space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Absolute continuity and singularity of two probability measures on a filtered space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-237161