Conditioning super-Brownian motion on its boundary statistics, and fragmentation

We condition super-Brownian motion on "boundary statistics" of the exit measure $X_D$ from a bounded domain $D$. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure $X_D$. Two particular examples are: conditioning on a Poisson random measure with intensity $\beta X_D$ and conditioning on $X_D$ itself. We find the conditional laws as $h$-transforms of the original SBM law using Dynkin's formulation of $X$-harmonic functions. We give explicit expression for the (extended) $X$-harmonic functions considered. We also obtain explicit constructions of these conditional laws in terms of branching particle systems. For example, we give a fragmentation system description of the law of SBM conditioned on $X_D=\nu$, in terms of a particle system, called the backbone. Each particle in the backbone is labeled by a measure $\tilde{\nu}$, representing its descendants' total contribution to the exit measure. The particle's spatial motion is an $h$-transform of Brownian motion, where $h$ depends on $\tilde{\nu}$. At the particle's death two new particles are born, and $\tilde{\nu}$ is passed to the newborns by fragmentation.Comment: Published in at http://dx.doi.org/10.1214/12-AOP778 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Türkiye'de ülke içinde yerinden edilme sorunu: tespitler ve çözüm önerileri = The problem of internal displacement in Turkey: assessment and policy proposals

Bu rapor, Doç. Dr. A. Tamer Aker (psikiyatr, Kocaeli Üniversitesi), Yrd. Doç. Dr. A. Betül Çelik (siyaset bilimci, Sabancı Üniversitesi), Dilek Kurban (hukuk doktoru, TESEV), Doç. Dr. Turgay Ünalan (nüfusbilimci, Hacettepe Üniversitesi) ve Yrd. Doç. Dr. H. Deniz Yükseker'den (sosyolog, Koç Üniversitesi) oluşan TESEV Ülke İçinde Yerinden Edilme Araştırma ve İzleme Grubu tarafından hazırlanmıştır. Grup, yerinden edilmeyi çatışma ortamının keskinleştirdiği devlet merkezli düşünüşün ve çeşitli ideolojik kamplaşmaların ötesinde, yurttaşlık haklarının yeniden tesisi ve toplumsal rehabilitasyon eksenlerinde ve insani boyutları bağlamında ele almaktadır