Ergodic control of multidimensional diffusions I: the existence results

The existence of optimal stable Markov relaxed controls for the ergodic control of multidimensional diffusions is established by direct probabilistic methods based on a characterization of a.s. limit sets of empirical measures. The optimality of the above is established in the strong (i.e., almost sure) sense among all admissible controls under very general conditions

Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the non zerosum case we have proved the existence of a Nash equilibrium

Prediction of preeclampsia by a combination of maternal spot urinary protein-creatinine ratio and uterine artery doppler

Background: Preeclampsia (PE) is heterogeneous disorder. The aim of the study was to observe the role of a spot urinary protein - creatinine ratio (UPCR) and uterine artery doppler velocimetry measured between 20-24 weeks of gestation in prediction of preeclampsia.Methods: Prospective observational study conducted on 120 pregnant mothers with singleton pregnancy between 20-24 weeks of gestational age in two tertiary teaching hospitals in eastern India. A spot urinary protein creatinine ratio (UPCR) was determined in a mid- stream urine sample and estimation of protein was done by immunoturbidimetric micro albumin method and creatinine by modified Jaffe’s method. Doppler velocimetry was also determined at 20-24 weeks of gestation. A notch in uterine artery, unilateral or bilateral; or RI > 0.7 and PI of > 1.45 were considered to have an abnormal result. Women were followed-up and relationship between variables was assessed by Chi- square test.Results: Women who subsequently developed preeclampsia had significantly higher UPCR (median 44.8 mg/mmol) when compared with women of unaffected groups (median 26.6 mg/mmol). The optimum spot urinary UPCR to predict preeclampsia was 35.5 mg/mmol and the cut-off value >35.5 mg/mmol had a test sensitivity (80%), specificity (94.06%), PPV (66.76%) and NPV (96.94%).The area under curve (AUC) of spot UPCR in ROC curve was  0.949 (95% CI,0.891 - 1.000). For predicting preeclampsia, the mean uterine artery RI had to be >0.7 having sensitivity (60%), specificity (97.03%), PPV (75%) and NPV (94.23%). The area under curve (AUC) was 0.856 (95% CI, 0.742 - 0.971).Conclusions: Second trimester UA doppler is a useful screening test for prediction of preeclampsia. This test works best when combined with a spot UPCR and accuracy of both the methods for prediction of preeclampsia was 92.24%