Explicit Stationary Distribution of the （L, 1）-reflecting Random Walk on the Half Line

In this paper,we consider the（L,1） state-dependent reflecting random walk（RW） on the half line,which is an RW allowing jumps to the left at a maximal size L.For this model,we provide an explicit criterion for（positive） recurrence and an explicit expression for the stationary distribution.As an application,we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions.The main tool employed in the paper is the intrinsic branching structure within the（L,1）-random walk.     

Assessing the reliability of a nanocomponent using nanocrack growth

In nanoscience and nanotechnology, much attention has been given to the dual problem of designing nanocomponents with novel physical properties and how such nanocomponents can be fabricated. Receiving less attention has been the question of the nanocomponent's reliability; how does a nanocomponent fail and how long does a nanocomponent survive under typical operating conditions? High reliability is necessary to guarantee the advancement and utilization of nanocomponents due to the fact that they account for a high proportion of costs of newly designed nanosystems as well as multiscale systems. A nanocomponent is a component that is made of atoms, and its reliability is determined by these atoms. There are situations where it is hard or impossible to extract information from a nanocomponent about its relationship to its atoms. In this article, we assess the nanocomponent's reliability by using its physical properties. Specifically, it is known that nanocrack growth involves considerable statistical variability and such variability should be accounted for assessing growth. In this paper, we first provide a stochastic nanocrack growth model and then evaluate the reliability of a nanocomponent based on this model. Various properties of this model are obtained. We also evaluate the reliability of a nanocomponent under different assumptions on our proposed growth model. This paper is a modification of the extensive literature on modeling fatigue cracks in materials on a larger scale, applied to nanoscale where growth is not a function of cumulative stress on the component but related to the time to first exceedance of a threshold. Copyright © 2013 John Wiley & Sons, Ltd.     

Dividends in finite time horizon

In this paper, we consider the classical risk model modified in two different ways by the inclusion of a dividend barrier. For Model I, we present numerical algorithms, which can be used to approximate or bound the expected discounted value of dividends up to a finite time horizon, t, or ruin if this occurs earlier. We extend this by requiring the shareholders to provide the initial capital and to pay the deficit at ruin each time it occurs so that the process then continues after ruin up to time t. For Model I, we assume the full premium income is paid as dividends whenever the surplus exceeds a set level. In our Model II, we assume dividends are paid at a rate less than the rate of premium income. Copyright © 2012 John Wiley & Sons, Ltd.     

Pricing a stochastic car value depreciation deal

This paper deals with pricing a contract under which a dealer buys back a car from a client, for a cash amount contained in a given depreciation table. The value of the car is supposed to depreciate according to a stochastic model with random repairs modeled by a Poisson process. Copyright © 2013 John Wiley & Sons, Ltd.     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.     

A novel cognitive system model and approach to transformation of information granules

In this paper, a novel cognitive system model is established based on formal concept analysis to exactly describe human cognitive processes. Two new operators, extent–intent and intent–extent, are introduced between an object and its attributes. By analyzing the necessity and sufficient relations between the object and some of its attributes, the information granule concept is investigated in human cognitive processes. Furthermore, theories of transforming arbitrary information granule into necessary, sufficient, sufficient and necessary information granules are addressed carefully. Algorithm of the transformation is constructed, by which we can provide an efficient approach to the conversion among information granules. To interpret and help understand the theories and algorithm, an experimental computing program is designed and two cases is employed as case study. Results of the small scale case are calculated by the method presented in this paper. The large-scale case is calculated by the experimental computing program and validated by the proposed algorithm. The considered framework can provide a novel convenient tool for artificial intelligence researches.     

Discrete-space partial dynamic equations on time scales and applications to stochastic processes

We consider a general class of discrete-space linear partial dynamic equations. The basic properties of solutions are provided (existence and uniqueness, sign preservation, maximum principle). Above all, we derive the following main results: first, we prove that the solutions depend continuously on the choice of the time scale. Second, we show that, under certain conditions, the solutions describe probability distributions of nonhomogeneous Markov processes, and that their time integrals remain the same for all underlying regular time scales.     

基于ANP的装备质量管理风险评估模型

根据装备质量管理的特点对装备质量管理的风险因素进行了分析,依据指标体系的设计原则建立了装备质量管理风险评估的指标体系,并给出了基于网络层次分析法和粒子群优化算法的的装备质量管理风险评估指标权重值的确定方法.并给出了实例分析.     

修理工单重定期休假可修系统更换模型研究

针对修理工带有单重休假的单部件可修系统,提出了一种新的维修更换模型.假定系统是可修的,逐次故障后的维修时间构成随机递增的几何过程,系统工作时间构成随机递增的几何过程,在修理工休假时间为定长的情况下,分别选取系统的总工作时间T和故障维修次数N为更换策略,以长期运行单位时间内的期望效益为目标函数,通过更新过程和几何过程理论建立数学模型,导出了目标函数的解析表达式,通过最大化目标函数来获取系统最优的更换策略T*和N*.并在一定条件下给出了策略N比策略T优的充分条件.最后,通过数值例子验证了方法的有效性.     

改性松香键合二氧化硅高效液相色谱固定相的制备及其对三七总皂苷的分离

三七中发挥药效的主要成分为三七皂苷R1、人参皂苷Rg1、人参皂苷Re、人参皂苷Rb1和人参皂苷Rd,用于贫血、冠心病、高血压、脑卒中后遗症等疾病的治疗,但其化学成分多且难分离.将氢化松香丙烯酸羟乙酯(HRHA)通过巯基-烯点击化学反应键合到烷基化硅胶表面,制备出一种新型的改性松香键合二氧化硅高效液相色谱固定相(SiO2...