Projections, Pseudo-Stopping Times and the Immersion Property

Given two filtrations $\mathbb F \subset \mathbb G$, we study under which conditions the $\mathbb F$-optional projection and the $\mathbb F$-dual optional projection coincide for the class of $\mathbb G$-optional processes with integrable variation. It turns out that this property is equivalent to the immersion property for $\mathbb F$ and $\mathbb G$, that is every $\mathbb F$-local martingale is a $\mathbb G$-local martingale, which, equivalently, may be characterised using the class of $\mathbb F$-pseudo-stopping times. We also show that every $\mathbb G$-stopping time can be decomposed into the minimum of two barrier hitting times

Integrational Justice: South America’s Experience

Integration justice is the result of supranational courts work in the framework of states’ regional economic unions. The resolution of disputes between states, supranational institutions and economic entities in the framework of the common market of South American countries (Mercosur) and the Andean community is of considerable interest in terms of comparative analysis of similar practices in the European Union and the Eurasian Economic Union. The international integration practice has shown that the legal force, binding nature and direct action of decisions of supranational courts are necessary to bring the national legal systems of the member states of integration associations to a harmonized rule of law

The most effective but largely ignored target for prostate cancer early detection and intervention

Over the past two decades, the global efforts for the early detection and intervention of prostate cancer seem to have made significant progresses in the basic researches, but the clinic outcomes have been disappointing: (1) prostate cancer is still the most common non-cutaneous cancer in Europe in men, (2) the age-standardized prostate cancer rate has increased in nearly all Asian and African countries, (3) the proportion of advanced cancers at the diagnosis has increased to 8.2% from 3.9% in the USA, (4) the worldwide use of PSA testing and digital rectal examination have failed to reduce the prostate cancer mortality, and (5) there is still no effective preventive method to significantly reduce the development, invasion, and metastasis of prostate cancer… Together, these facts strongly suggest that the global efforts during the past appear to be not in a correlated target with markedly inconsistent basic research and clinic outcomes. The most likely cause for the inconsistence appears due to the fact that basic scientific studies are traditionally conducted on the cell lines and animal models, where it is impossible to completely reflect or replicate the in vivo status. Thus, we would like to propose the human prostate basal cell layer (PBCL) as “the most effective target for the early detection and intervention of prostate cancer”. Our proposal is based on the morphologic, immunohistochemical and molecular evidence from our recent studies of normal and cancerous human prostate tissues with detailed clinic follow-up data. We believe that the human tissue-derived basic research data may provide a more realistic roadmap to guide the clinic practice and to avoid the potential misleading from in vitro and animal studies

Bayesian switching multiple disorder problems

The switching multiple disorder problem seeks to determine an ordered infinite sequence of times of alarms which are as close as possible to the unknown times of disorders, or change-points, at which the observable process changes its probability characteristics. We study a Bayesian formulation of this problem for an observable Brownian motion with switching constant drift rates. The method of proof is based on the reduction of the initial problem to an associated optimal switching problem for a three-dimensional diffusion posterior probability process and the analysis of the equivalent coupled parabolic-type free-boundary problem. We derive analytic-form estimates for the Bayesian risk function and the optimal switching boundaries for the components of the posterior probability process