Mean-field backward stochastic differential equations: A limit approach

Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application in Economics, Finance and Game Theory. The objective of our paper is to investigate a special mean-field problem in a purely stochastic approach: for the solution $(Y,Z)$ of a mean-field backward stochastic differential equation driven by a forward stochastic differential of McKean--Vlasov type with solution $X$ we study a special approximation by the solution $(X^N,Y^N,Z^N)$ of some decoupled forward--backward equation which coefficients are governed by $N$ independent copies of $(X^N,Y^N,Z^N)$. We show that the convergence speed of this approximation is of order $1/\sqrt{N}$. Moreover, our special choice of the approximation allows to characterize the limit behavior of $\sqrt{N}(X^N-X,Y^N-Y,Z^N-Z)$. We prove that this triplet converges in law to the solution of some forward--backward stochastic differential equation of mean-field type, which is not only governed by a Brownian motion but also by an independent Gaussian field.Comment: Published in at http://dx.doi.org/10.1214/08-AOP442 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discussion on Application of Nursing Risk Management in Physical Examination Center

Objective: to explore whether the application of nursing risk management in physical examination center has positive significance; Method: 50 patients who received medical examination from December 1st to 31st, 2019 were randomly divided into two groups according to the number of the medical examination card, 25 patients in Group A were given routine nursing management, which will be referred as the control group hereafter while group B with 25 people will have the nursing risk management, which will be referred as the observation group. After all the physical examination items ended, statistical physical examination results and the degree of satisfaction of the physical examination will be recorded. Results: Errors of the observation group in the physical examination process were significantly less than that of the control group (P<0.05) and the degree of satisfaction of physical examinees in the observation group was higher than that in the control group(P<0.05). Conclusion: The use of nursing risk management in medical examination center can improve the degree of satisfaction of medical examiners and reduce the occurrence of accidents and disputes

Possible link of a structurally driven spin flip transition and the insulator-metal transition in the perovskite La1−x_{1-x}Bax_{x}CoO3_{3}

The complex nature of the magnetic ground state in La$_{1-x}$A$_{x}$CoO$_{3}$ (A = Ca, Sr, Ba) has been investigated via neutron scattering. It was previously observed that ferromagnetic (FM) as well as antiferromagnetic (AFM) correlations can coexist prior to the insulator-metal transition (IMT). We focused on a unique region in the Ba phase diagram, from x = 0.17 - 0.22, in which a commensurate AFM phase appears first with a propagation vector, k = (0, -0.5, 0.5), and the Co moment in the (001)$_{R}$ plane of the rhombohedral lattice. With increasing x, the AFM component weakens while an FM order appears with the FM Co moment directed along the (001)$_{R}$ (=(111)$_{C}$) axis. By x = 0.22, a spin flip to new FM component appears as the crystal fully transforms to an orthorhombic (Pnma) structure, with the Co moments pointing along a new direction, (001)$_{O}$ (=(110)$_{C}$). It is the emergence of the magnetic Pnma phase that leads to IMT.Comment: 5 page

Clinical application of retinal oscillatory potential

Retinal oscillatory potential has been widely applied in diagnosis, condition variety and prognostic of eye disease. It is believed that oscillatory potentials are generated from the inner retina, and can objectively reflect blood circulation in inner retina. Now the applications and prospects of retinal oscillatory potential are briefly introduced, in order to promote the popularity of this technology