Strong uniqueness for stochastic evolution equations with unbounded measurable drift term

We consider stochastic evolution equations in Hilbert spaces with merely measurable and locally bounded drift term $B$ and cylindrical Wiener noise. We prove pathwise (hence strong) uniqueness in the class of global solutions. This paper extends our previous paper (Da Prato, Flandoli, Priola and M. Rockner, Annals of Prob., published online in 2012) which generalized Veretennikov's fundamental result to infinite dimensions assuming boundedness of the drift term. As in our previous paper pathwise uniqueness holds for a large class, but not for every initial condition. We also include an application of our result to prove existence of strong solutions when the drift $B$ is only measurable, locally bounded and grows more than linearly.Comment: The paper will be published in Journal of Theoretical Probability. arXiv admin note: text overlap with arXiv:1109.036

Continuity equation in LlogL for the 2D Euler equations under the enstrophy measure

The 2D Euler equations with random initial condition has been investigates by Albeverio and Cruzeiro (Commun Math Phys 129:431–444, 1990) and other authors. Here we prove existence of solutions for the associated continuity equation in Hilbert spaces, in a quite general class with LlogL densities with respect to the enstrophy measure

The effects of childbirth on the pelvic-floor

Basically, vaginal delivery is associated with the risk of pelvic floor damage. The pelvic floor sequelae of childbirth includes anal incontinence, urinary incontinence and pelvic organ prolapse. Pathophysiology, incidence and risk factors for the development of the respective problems are reviewed. Where possible, recommendations for reducing the risk of pelvic floor damage are given

Effects of carrying a pregnancy and of method of delivery on urinary incontinence: a prospective cohort study

BACKGROUND: This study was carried out to identify risk factors associated with urinary incontinence in women three months after giving birth. METHODS: Urinary incontinence before and during pregnancy was assessed at study enrolment early in the third trimester. Incontinence was re-assessed three months postpartum. Logistic regression analysis was used to assess the role of maternal and obstetric factors in causing postpartum urinary incontinence. This prospective cohort study in 949 pregnant women in Quebec, Canada was nested within a randomised controlled trial of prenatal perineal massage. RESULTS: Postpartum urinary incontinence was increased with prepregnancy incontinence (adjusted odds ratio [adj0R] 6.44, 95% CI 4.15, 9.98), incontinence beginning during pregnancy (adjOR 1.93, 95% CI 1.32, 2.83), and higher prepregnancy body mass index (adjOR 1.07/unit of BMI, 95% CI 1.03,1.11). Caesarean section was highly protective (adjOR 0.27, 95% CI 0.14, 0.50). While there was a trend towards increasing incontinence with forceps delivery (adjOR 1.73, 95% CI 0.96, 3.13) this was not statistically significant. The weight of the baby, episiotomy, the length of the second stage of labour, and epidural analgesia were not predictive of urinary incontinence. Nor was prenatal perineal massage, the randomised controlled trial intervention. When the analysis was limited to women having their first vaginal birth, the same risk factors were important, with similar adjusted odds ratios. CONCLUSIONS: Urinary incontinence during pregnancy is extremely common, affecting over half of pregnant women. Urinary incontinence beginning during pregnancy roughly doubles the likelihood of urinary incontinence at 3 months postpartum, regardless whether delivery is vaginal or by Caesarean section

On a class of infinite-dimensional singular stochastic control problems

none4We study a class of infinite-dimensional singular stochastic control problems that might find applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially ordered infinite-dimensional space X, it takes values in the positive cone of X, and it has right-continuous and nondecreasing paths. Our main contribution is to provide a rigorous formulation of the problem by properly defining the controlled dynamics and integrals with respect to the control process, and then to derive necessary and sufficient first-order conditions for optimality. The latter are finally exploited in a specification of the model where we determine an optimal control. The techniques used are those of semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.noneFederico S.; Ferrari G.; Riedel F.; Rockner M.Federico, S.; Ferrari, G.; Riedel, F.; Rockner, M