Singular mean-field control games

This article studies singular mean field control problems and singular mean field two-players stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some assumptions the optimality conditions for singular mean-field control are reduced to a reflected Skorohod problem, whose solution is proved to exist uniquely. Motivations are given as optimal harvesting of stochastic mean-field systems, optimal irreversible investments under uncertainty and mean-field singular investment games. In particular, a simple singular mean-field investment game is studied, where the Nash equilibrium exists but is not unique.     

A moderate deviation principle for 2-D stochastic Navier–Stokes equations driven by multiplicative Lévy noises

In this paper, we establish a moderate deviation principle for two-dimensional stochastic Navier–Stokes equations driven by multiplicative Lévy noises. The weak convergence method introduced by Budhiraja, Dupuis and Ganguly in [3] plays a key role.     

Algebras of Jordan brackets and generalized Poisson algebras

We construct bases for free unital generalized Poisson superalgebras and for free unital superalgebras of Jordan brackets. Also, we prove an analogue of Farkas’ theorem for PI unital generalized Poisson algebras and PI unital algebras of Jordan brackets. Relations between generic Poisson superalgebras and superalgebras of Jordan brackets are studied.     

大数据背景下的商品需求预测与分仓规划

商品需求预测对于电商企业意义重大,对阿里电商平台的交易数据进行挖掘以获取有效特征,利用特征建立模型对未来两周这些商品的需求进行动态预测,并基于预测结果和成本最小的原则提出分仓规划建议.预测模型选择随机森林做回归,然后在残差分析的基础上建立报童模型求解分仓的库存规划.对特征数量众多的电商交易数据挖掘所建立的模型有助于电商企业进行有效的商品需求预测并据此制定成本更低的分仓规划.     

广义泊松回归模型的推广及其在医疗保险中应用

计数数据往往存在过离散(over-dispersed)即方差大于均值特征,若利用传统的泊松回归模型拟合数据往往会导致其参数的标准误差被低估,显著性水平被高估的错误结论。负二项回归模型、广义泊松回归模型通常被用来处理过离散特征数据。本文以两类广义泊松回归模型GP-1和GP-2模型为基础,将其推广为更为一般的GP-P形式,其中P为参数。此时,P=1或P=2,GP-P模型就退化为GP-1和GP-2模型。文中最后利用此类推广的GP-P模型处理了一组医疗保险数据,并与泊松回归模型、负二项回归模型拟合结果进行了比较。结果表明,推广后的GP-P模型的拟合效果更优。     

Using 3D Composite Electrode Materials for Electricity Generation from Swine Wastewater in a Dual‐Chamber Microbial Fuel Cells

Swine wastewater has a high concentration of organic matter, suspended solids, and higher ammonia nitrogen, odor, complex polluting ingredients, and large emissions. A two‐chambered cubic microbial fuel cell (MFC) was used to evaluate the effect of a novel three‐dimensional (3D ) electrode made of 3D iron composites and 3D stainless composites on the electricity generation. Swine wastewater with a total chemical oxygen demand (TCOD ) of 3688 ± 300 mg/L was used as the feedstock in the anode chamber. The MFC reactor was incubated with an initial pH of 7.0 in an air shaker with a temperature of ~35°C and 100 rpm in the fed‐batch mode. A fixed external resistance (R ) of 100 Ω was connected between the electrodes, and the closed‐circuit potentials of the MFCs were recorded every 5 min. The results showed that using an iron–carbon fiber composite 3D electrode resulted in a peak electricity generation of 321 mV on the first 2 days and maintained a stable voltage of 163 mV during the second to sixth days. The COD removal efficiency could reach 75%. Using a stainless–carbon fiber 3D electrode could generate a peak voltage of only 29.5 mV and a stable voltage of 15.2 mV with a COD removal efficiency of 54%.     

Successive approximation of infinite dimensional semilinear backward stochastic evolution equations with jumps

In this paper, we study the existence and uniqueness of mild solutions to semilinear backward stochastic evolution equations driven by the cylindrical I$I$-Brownian motion and the Poisson point process in a Hilbert space with non-Lipschitzian coefficients by the successive approximation.     

On tails of stationary measures on a class of solvable groups

Let G be a subgroup of GL(R,d) and let (Qn,Mn) be a sequence of i.i.d. random variables with values in Rd?G and law μ. Under some natural conditions there exists a unique stationary measure ν on Rd of the process Xn=MnXn−1+Qn. Its tail properties, i.e. behavior of as t tends to infinity, were described some over thirty years ago by H. Kesten, whose results were recently improved by B. de Saporta, Y. Guivarc'h and E. Le Page. In the present paper we study the tail of ν in the situation when the group G₀ is Abelian and Rd is replaced by a more general nilpotent Lie group N. Thus the tail behavior of ν is described for a class of solvable groups of type NA, i.e. being semi-direct extension of a simply connected nilpotent Lie group N by an Abelian group isomorphic to Rd. Then, due to A. Raugi, (N,ν) can be interpreted as the Poisson boundary of (NA,μ).