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Solar cell is the basic component of satellite photovoltaic panels with complicated redundant system structure. Its reliability plays an important role in the system, and its performance shows a degradation trend over time. In this paper, study is conducted for the solar cell degradation modeling and reliability analysis basedon practical testing results. Specifically, we illustrate an accelerated test for the attenuation ratio character test under different accumulativeirradiation levels, focusing on the heteroscedasticity of the collected testing data. A heteroscedastic linear model is proposed, and the lifedistribution of the photovoltaic panel is obtained by using Fiducial method. A numerical example is shown for the purpose of illustration.     

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In this paper, we consider the estimation problemfor partially linear models with additive measurement errors in thenonparametric part. Two kinds of estimators are proposed. The first oneis an integral moment-based estimator with deconvolution kernel techniques,associated with the strong consistency for the estimator. Another oneis a simulation-based estimator to avoid the integrals involved in theintegral moment-based estimator. Simulation studies are conducted toexamine the performance of the proposed estimators.     

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For a financial or insurance entity, the problem of finding the optimal dividend distribution strategy and optimal firm value function is a widely discussed topic. In the present paper, it is assumed that the firm faces two types of liquidity risks: a Brownian risk and a Poisson risk. The firm can control the time and amount of dividends paid out to shareholders. By sufficiently taking into account the safety of the company, bankruptcy is said to take place at time $t$ if the cash reserve of the firm runs below the linear barrier b+kt (not zero), see 1. We deal with the problem of maximizing the expected total discounted dividends paid out until bankruptcy. The optimal dividend return (or, firm value) function is identified as the classical solution of the associated Hamilton-Jacobi-Bellman (HJB) equation where a second-order differential-integro equation is involved. By solving the corresponding HJB equation, the analytical solution of the optimal firm value function is obtained, the optimal dividend strategy is also characterized, which is of linear barrier type: at time t the firm keeps cash inside when the cash reserves level is less than a critical linear barrier and pays cash in excess of this linear barrier as dividends.     

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In this note we discuss uniform integrability of random variables. In a probability space, we introduce two new notions on uniform integrability of random variables, and prove that they are equivalent to the classic one. In a sublinear expectation space, we give de La Vall\'{e}e Poussin criterion for the uniform integrability of random variables and do some other discussions.     

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??This paper considers the expected penalty functions for a discrete semi-Markov risk model, which includes several existing risk models such as the compound binomial model (with time-correlated claims) and the compound Markov binomial model (with time-correlated claims) as special cases. Recursive formulae and the initial values for the discounted free penalty functions are derived in the two-state model by an easy method. We also give some applications of our results.     

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In the situation of rho-mixing dependent sequences, this paper studied the mean square error and the optimal bandwidth of distribution kernel estimator nu_{p,h} of VaR. And the optimal bandwidth minimized the mean square error. The density function of Laplace distribution is used in the calculation of bandwidthand we adopt the method of interpolation to compute specific value of bandwidth in this paper. According to the numerical simulations, the distribution kernel estimator is more accurate by comparing the performance of VaR distribution kernel estimation with a common order statistic. Finally, Shangzheng A-share index and Shenzheng B-share index are chosen for an empirical research, which concludes that the risk of the latter is significantly higher than that of the former.     

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We study a birth and death process $\{N_t\}_{t\ge0}$ in i.i.d. random environment, for which at each discontinuity, one particle might be born or at most $L$ particles might be dead. Along with investigating the existence and the recurrence criterion, we also study the law of large numbers of $\{N_t\}$. We show that the first passage time can be written as a functional of an $L$-type branching process in random environment and a sequence of independent and exponentially distributed random variables. Consequently, an explicit velocity of the law of large numbers can be given.     

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or the variance parameter of the normal distribution with a normal-inverse-gamma prior, we analytically calculate the Bayes posterior estimator with respect to a conjugate normal-inverse-gamma prior distribution under Stein's loss function. This estimator minimizes the Posterior Expected Stein's Loss (PESL). We also analytically calculate the Bayes posterior estimator and the PESL under the squared error loss function. The numerical simulations exemplify our theoretical studies that the PESLs do not depend on the sample, and that the Bayes posterior estimator and the PESL under the squared error loss function are unanimously larger than those under Stein's loss function. Finally, we calculate the Bayes posterior estimators and the PESLs of the monthly simple returns of the SSE Composite Index.     

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Credit valuation adjustment is the price adjustment of financial contract considering possible default of counterparty and it is an important way to measure counterparty risk. It is the key to establish a reasonable default dependence structure model. We introduce an economic state variable and shot noise processes in a Markov copula model and establish a regime switching Markov copula model with shot noise, where we can not only describe the impact of common economic conditions characteristics but also describe the credit name's characteristic. In this proposed model, we study martingale property of the model and the collateralized CVA of credit default swaps, and furthermore, we perfer some numerical calculations on the collateralized CVA and examine the impact of some model parameters on the CVA.     

具有不同分布NA随机变量列的强大数律及应用

给出了具有不同分布的NA随机变量列满足的若干强大数律;作为应用,不仅将独立随机变量的一类强极限定理完整的推广到NA随机变量情形,而且关于NA随机变量的一些已有结果可以作为推论得出.     

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Strong laws of large numbers play key role in nonadditive probability theory. Recently, there are many research papers about strong laws of large numbers for independently and identically distributed (or negatively dependent) random variables in the framework of nonadditive probabilities (or nonlinear expectations). This paper introduces a concept of weakly negatively dependent random variables and investigates the properties of such kind of random variables under aframework of nonadditive probabilities and sublinear expectations. A strong law of large numbers is also proved for weakly negatively dependent random variables under a kind of sublinear expectation as an application     

关于两两NQD随机变量部分和强大数律的注记

In this paper, the authors study the strong law of large numbers for partial sums of pairwise negatively quadrant dependent （NQD） random variables. The results obtained improve the corresponding theorems of Hu et al. （2013）, and Qiu and Yang （2006） under some weaker conditions.     

NA随机变量列一类强大数律的充分必要条件

本文给出了具有不同分布NA随机变量列满足一类强大数律的充分必要条件, 从而将Egorov对独立随机变量列建立的结果推广到NA随机变量情形; 作为应用, 我们还建立了一个新的强大数律.     

分块m-负相依随机变量的Wittmann 型强大数律

本文得到了分块m-负相依随机变量的Wittmann 型强大数律,这些结果推广和改进了已知的一些文献中相关的结论.     

关于任意随机序列的一个强大数定理

This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained.     

随机环境中马氏链的大数定律和强大数定律

本文主要研究了单无限马氏环境中马氏链的几类特殊函数的大数定律及强大数定律,并且给出了加于链和过程特殊样本函数上的充分条件.     

对称随机变量序列的收敛性

讨论了对称的随机变量序列的完全收敛性与强大数律,改进和加强了独立同分布时Baum L E,Katz M及Bai Z D,Cheng P E相应的结果.     

关于~*-mixing随机变量序列的强大数定律

利用任意随机变量序列的强大数定律讨论 * -mixing随机变量序列的强大数定律 ,得到了该序列的一个强极限定理 ,推广了经典的 * mixing随机变量序列的强大数定律 .同时讨论了 m相依序列和独立随机变量序列的强大数定律 .