一类向量高斯过程之上穿过点过程的渐近分布

｛Ｘ（ｔ），ｔ≥｝为ｐ维高斯过程，在一定条件下，本文得到了｛Ｘ（ｔ），０≤ｔ≤Ｔ｝对水平ＵＴ（＞０）的ε－上穿过次数所形成的点过程的渐近分布（Ｔ→∞）。证明了Ｐ个分量点过程的渐近独立性。     

过程能力指数综述

统计过程控制是现代化工业生产中确保产品质量和可靠性的核心方法之一，而过程能力指数则是度量一个工业过程能力的重要指标．本文综述了过程能力指数的研究现状，首先介绍了过程能力指数的概念，然后较详细地介绍了几种主要的过程能力分析方法，并进一步说明了非正态分布的处理．最后给出了结论，并展望了过程能力指数今后的研究和发展方向．     

两指标Levy过程的强极限定理

本文研究了两指标Ｌｅｖ过程增量平方和的强极限，获得了一些重要结果。     

扩散过程的极性的一个充分条件

本文研究非退化多维扩散过程的极性，得到了一个充分条件。     

常利率下Cox风险过程的罚金折现期望函数

本文考虑了常利率环境下Cox风险模型的罚金折现期望值，利用后向差分法，得到了条件期望值与平稳情形时的期望值分别所满足的积分方程．并且，给出了一个强度过程为二状态马尔可夫过程及索赔服从指数分布的例子．     

带随机过程的随机规划问题——最优值过程与最优解集过程的鞅性

假设问题中所含随机过程为鞅，本文证明了带随机过程的随机规划问题共最优值过程与最优解集过程分别为实值上鞅与集值上鞅，且存在最优鞅通过程。     

索赔为一般到达的保险风险模型

本文应用作者们提出和建立的Markov骨架过程方法，研究了索赔为一般到达的保险风险模型，得到了破产时间分布以及破产时间与破产时刻前后资产盈科的联合分布，由此可计算出人们关心的一些重要指标。     

关于Q过程跳跃次数的一个注记

本文考虑一类Ｑ过程的跳次数及相应的点过程，证明了与此点过程有关的一个随机积分是平方可积鞅，同时对有关文献中的不足之处作了讨论。     

两物种超过程分枝特征的刻画

本文运用调和分析的方法，通过对二元连续函数的积分表示问题的研究，得到了一类两物种超过程的分枝特征的一般刻画。     

一类测试值分支过程的不变特性

空间齐次性是Ｒ＾ｄ上Ｌｅｖｙ过程的一个重要特性，本文考虑超Ｌｅｖｙ过程的类似性质，即是分布意义下的平移不变性，并且对一类特殊的测试值分支过程当其初始测试是Ｌｅｂｅｓｇｕｅ测度时，得到了更强的结果。     

Towards a Characterization of Markov Processes Enjoying the Time-Inversion Property

We give a necessary and sufficient condition for a homogeneous Markov process taking values in ℝ ⁿ to enjoy the time-inversion property of degree α. The condition sets the shape for the semigroup densities of the process and allows to further extend the class of known processes satisfying the time-inversion property. As an application we recover the result of Watanabe (Z. Wahrscheinlichkeitstheor. Verwandte Geb. 31:115–124, 1975) for continuous and conservative Markov processes on ℝ₊. As new examples we generalize Dunkl processes and construct a matrix-valued process with jumps related to the Wishart process by a skew-product representation.      

A note on the stationarity of a threshold first-order bilinear process

In the present note we study the threshold first-order bilinear model

X(t)=aX(t−1)+(b₁1_{X(t−1)<c}+b₂1_{X(t−1)c})X(t−1)e(t−1)+e(t), tεN

where {e(t), tεN} is a sequence of i.i.d. absolutely continuous random variables, X(0) is a given random variable and a, b₁, b₂ and c are real numbers. Under suitable conditions on the coefficients and lower semicontinuity of the densities of the noise sequence, we provide sufficient conditions for the existence of a stationary solution process to the present model and of its finite moments of order p.     

Optimal control of one dimensional non-conservative quasi-diffusion processes

An extension of the work of P. Mandl concerning the optimal control of time-homogeneous diffusion processes in one dimension is given. Instead of a classical second order differential operator as infinitesimal generator, Feller's generalized differential operator D_mD⁺_p with a possibly nondecreasing weight function m is used. In this manner an optimal control of a wider class of one dimensional Marcov processes-including diffusions as well as birth and death processes-is realized.     

Structure of the third moment of the generalized Rosenblatt distribution

The Rosenblatt distribution appears as limit in non-central limit theorems. The generalized Rosenblatt distribution is obtained by allowing different power exponents in the kernel that defines the usual Rosenblatt distribution. We derive an explicit formula for its third moment, correcting the one in Maejima and Tudor (2012) and Tudor (2013). Evaluating this formula numerically, we are able to confirm that the class of generalized Hermite processes is strictly richer than the class of Hermite processes.     

A stochastic production planning model with a dynamic chance constraint

This paper deals with the optimal production planning for a single product over a finite horizon. The holding and production costs are assumed quadratic as in Holt, Modigliani, Muth and Simon (HMMS) [7] model. The cumulative demand is compound Poisson and a chance constraint is included to guarantee that the inventory level is positive with a probability of at least α at each time point. The resulting stochastic optimization problem is transformed into a deterministic optimal control problem with control variable and of the optimal solution is presented. The form of state variable inequality constraints. A discussion the optimal control (production rate) is obtained as follows: if there exists a time t₁ such that t₁?[O, T]where T is the end of the planning period, then (i) produce nothing until t₁ and (ii) produce at a rate equal to the expected demand plus a ‘correction factor’ between t₁ and T. If t₁ is found to be greater than T, then the optimal decision is to produce nothing and always meet the demand from the inventory.     

The inspection paradox in renewal-reward processes

To explore the inspection paradox in the context of a renewal-reward process, we obtain asymptotic expressions for the mean and distribution function of the reward associated with the spread (total life) of the process. These results also yield a simplified demonstration of the elementary renewal-reward theorem.     

一维扩散过程的最优停止问题的研究

本文研究了一维扩散过程的最优停止问题,论证了W iener过程和几何布朗运动是F e ller过程,同时给出了一般扩散过程的处理方法.     

Approximations to permutation and exchangeable processes

We obtain weighted approximations by a Brownian bridge to permutation and exchangeable processes and to appropriately defined inverse processes. Our results provide as special cases useful weighted approximations to the uniform empirical and quantile processes and to generalized bootstrapped versions of these processes. A number of other applications are discussed. Our approach is based on the Skorokhod embedding for martingales.     

两个相关更新过程的一种新描述

研究了两个相关点过程之间相关性的描述。我们指出当两个点过程是泊淞过程时，相关系数能充分描述它们之间的相互关系。当两个点过程是更新过程时，相关系数随着时间窗口的变化而变化，是时间窗口的递增函数。于是我们提出用相关系数曲线来描述两个更新过程之间的相互关系。这些结论对优化神经网络的设计将是很有用的。