Series representations for densities functions of a family of distributions—Application to sums of independent random variables

Series representations for several density functions are obtained as mixtures of generalized gamma distributions with discrete mass probability weights, by using the exponential expansion and the binomial theorem. Based on these results, approximations based on mixtures of generalized gamma distributions are proposed to approximate the distribution of the sum of independent random variables, which may not be identically distributed. The applicability of the proposed approximations are illustrated for the sum of independent Rayleigh random variables, the sum of independent gamma random variables, and the sum of independent Weibull random variables. Numerical studies are presented to assess the precision of these approximations.     

Spectral collocation methods for nonlinear weakly singular Volterra integro‐differential equations

In this paper, a spectral collocation approximation is proposed for neutral and nonlinear weakly singular Volterra integro‐differential equations (VIDEs) with non‐smooth solutions. We use some suitable variable transformations to change the original equation into a new equation, so that the solution of the resulting equation possesses better regularity, and the the Jacobi orthogonal polynomial theory can be applied conveniently. Under reasonable assumptions on the nonlinearity, we carry out a rigorous error analysis in L^∞ norm and weighted L² norm. To perform the numerical simulations, some test examples (linear and nonlinear) are considered with nonsmooth solutions, and numerical results are presented. Further more, the comparative study of the proposed methods with some existing numerical methods is provided.     

Stability Analysis for the Numerical Simulation of Hybrid Stochastic Differential Equations

This paper is mainly concerned with the exponential stability of a class of hybrid stochastic differential equations–stochastic differential equations with Markovian switching (SDEwMSs). It first devotes to reveal that under the global Lipschitz condition, a SDEwMS is pth (p ∈ (0,1)) moment exponentially stable if and only if its corresponding improved Euler-Maruyama(IEM) method is pth moment exponentially stable for a suitable step size. It then shows that the SDEwMS is pth(p ∈ (0,1)) moment exponentially stable or its corresponding IEM method with small enough step sizes implies the equation is almost surely exponentially stable or the corresponding IEM method, respectively. In that sense, one can infer that the SDEwMS is almost surely exponentially stable and the IEM method, no matter whether the SDEwMS is pth moment exponentially stable or the IEM method. An example is demonstrated to illustrate the obtained results.     

财务脆弱性问题的报童模型

在品牌渠道体系的建设过程中,除了对利润最大化的追求以外,财务上的脆弱性／柔性会极大地影响着经销商的决策心理和商业行为实践。本文着重考察单位产品利润率和剩余产品处理费用对经销商决策心理和行为的影响,通过分析零售商的收益分布状况,再基于展望理论的思路,建立了参考点取决于损益状况的报童展望模型。最后证明,财务脆弱性将更大地发挥损失厌恶型决策者的保守心理。     

Multivariate irregular sampling theorem

In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.     

限制性集合矩阵的计数公式

In this paper, we consider the counting problem of matrix of set (Aij)k×n which satisfies k∪i=1 n∪j=1 Aij={a1,a2,…,am} and other conditions, and obtain some computational formulas which extend all the results in [1].     

基于矩分析的资产组合选择

在风险资产收益分布为非正态的情景下,通过矩分析,研究其收益的高阶矩对资产组合选择的影响.首先,假设风险资产收益存在有限阶矩,泰勒展开边际财富期望效用,获得静态资产组合选择的近似解;其次,假设收益过程的跳跃产生收益分布的非正态性,运用随机控制方法获得动态资产组合选择的近似解析解,从高阶矩角度解释其特征。分析表明,超出峰度的存在导致减少风险资产投资,正(负)的偏度导致增加(减少)风险资产投资,该影响性随着它们及风险规避系数的增大而增强;可预测性导致资产组合存在正或负的对冲需求,取决于相关系数的符号和风险规避系数;跳跃性总体上减少风险资产投资;可预测性和跳跃性对动态资产组合选择的影响具有内在关联性。     

Spectrum is periodic for n-intervals

In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case.     

具交叉感染的流行病模型的数学分析

In this paper,an initial boundary value problem with homogeneous Neumann boundary condition is studied for a reaction-diffusion system which models the spread of infectious diseases within two population groups by means of self and criss-cross infection mechanism. Existence,uniqueness and boundedness of the nonnegative global solution (u1,u2,u3,u4),existence of the limit of the solution as t→+∞,namely,(u1,u2,u3,u4)→(u*1,0,u*3,0),are proved.