A maximum principle for fully coupled stochastic control systems of mean-field type

The present paper considers an optimal control problem for fully coupled forward–backward stochastic differential equations (FBSDEs) of mean-field type in the case of controlled diffusion coefficient. Moreover, the control domain is not assumed to be convex. By virtue of a reduction method, we establish the necessary optimality conditions of Pontryagin's type. As an application, a linear–quadratic stochastic control problem is studied.     

非李普希茨条件下无穷维随机微分方程的适度解

通过构造收敛的逼近列的方法给出了非李普希茨条件下无穷维随机微分方程dX=[AX+f(X)]dt+[BX+g(X)]dW的适度解的存在唯一性定理.文章推广了[1]和[2]的结论.     

一类线性混合模型的谱分解估计

谱分解估计(SDE)是新近提出的关于线性混合模型参数的一种新的估计方法,此方法的一个突出特点是同时给出固定效应参数和方差分量的显式解估计．本文就含两个方差分量的线性混合模型,对谱分解估计的性质做了进一步的研究,获得了方差分量的SDE和方差分析估计相等的充分必要条件,证明了在一定的条件下方差分量的SDE为一致最小方差无偏估计．     

STABILITY OF THE MILD SOLUTION OF STOCHASTIC NONLINEAR EVOLUTION DIFFERENTIAL EQUATIONS

In this paper, we consider the stability problem associated with the mild solutions of stochastic nonlinear evolution differential equations in Hilbert space under hypothesis which is weaker than Lipschitz condition. And the result is established by employing the Ito-type inequality and the extension of the Bihari's inequality.     

鸢尾根致香成分分析及在造纸法再造烟叶中的应用

采用同时蒸馏萃取法,从鸢尾根中提取致香成分,对其主要化学成分进行GC/MS分析,用鸢尾根致香成分进行了造纸法再造烟叶加香试验,并将加香后的造纸法再造烟叶样品添加在卷烟配方中进行评吸。结果表明,鸢尾根致香成分中共鉴定出17个化合物,主要含有癸酸和棕榈酸;鸢尾根致香成分能改善造纸法再造烟叶的烟气品质,并具有降低刺激的作用,加香后的造纸法再造烟叶在卷烟中应用也具有相同的效果。     

具有随机加速度的随机运动的存在性

讨论了随机加速度为位移的给定函数的随机运动的存在性(即R上的随机微分方程弱解的存在性),给出并证明了具有随机加速度的随机运动存在的几个充分性条件.     

Long time behavior of a mean-field model of interacting neurons

We study the long time behavior of the solution to some McKean–Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the asymptotic dynamic of the membrane potential of a spiking neuron in a large network. We prove that for a small enough interaction parameter, any solution converges to the unique (in this case) invariant probability measure. To this aim, we first obtain global bounds on the jump rate and derive a Volterra type integral equation satisfied by this rate. We then replace temporary the interaction part of the equation by a deterministic external quantity (we call it the external current). For constant current, we obtain the convergence to the invariant probability measure. Using a perturbation method, we extend this result to more general external currents. Finally, we prove the result for the non-linear McKean–Vlasov equation.     

Stability of stochastic differential equation with linear fractal noise

We study a class of stochastic differential equation with linear fractal noise. By an auxiliary stochastic differential equation, we prove the existence and uniqueness of the solution under some mild assumptions. We also give some estimates of moments of the solution. The exponential stability of the solution is discussed.