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This paper considers the asymptotics of randomly weighted sums and their maxima, where the increments {X_i,igeq1} is a sequence of independent, identically distributed and real-valued random variables and the weights {theta_i,igeq1} form another sequence of non-negative and independent random variables, and the two sequences of random variables follow some dependence structures. When the common distribution F of the increments belongs to dominant variation class, we obtain some weakly asymptotic estimations for the tail probability of randomly weighted sums and their maxima. In particular, when the Fbelongs to consistent variation class, some asymptotic formulas is presented. Finally, these results are applied to the asymptotic estimation for the ruin probability.     

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In this paper, we introduce the definitions of geometric strongly ergodic, strongly ergodic and weakly ergodic for continuous-state Markov chains, then we give a primary proof of equivalence of the ergodicities for continuous-state Markov chains.     

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Let p_M(t,x,y) be the minimal heat kernel of a d-dimenional compact Riemannian manifold M for any time tin(0,1] and x,yin M. Using the horizontal Brown bridge on M, we prove that, for any nonnegative integers n and m, there is a constant C depending on n,m and the manifold M, such that |nabla^n_xnabla^m_yln p_M(t,x,y)|leq C[d(x,y)/t+1/sqrt{t},]^{n+m}$, which generalizes the conclusion of the higher derivatives of the logarithmic heat kernel ln p_M(t,x,y) about single variable in ncite{1}.     

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This paper studies the estimation of change point in mean and variance function of a non-parametric regression model based on kernel estimation and wavelet method. First, kernel estimation of mean function is developed and it is used to estimate the position and jump size of mean change. Second, wavelet methods are applied to derive the variance estimator which is used to estimate the location and jump size of the change point in variance. The asymptotic properties of these estimators are proved. Finally, the results from a numerical simulations and comparison study show that validate the effectiveness of our method.     

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VaR风险度量在金融、保险中有重要的应用.本文建立了贝叶斯模型, 在某种损失函数下研究了VaR风险度量的贝叶斯估计.证明了指数-伽马分布下贝叶斯估计的强相合性和渐近正态性,最后利用数值模拟的方法验证了不同样本容量下估计的收敛速度.     

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Let, be two independent,
-dimensional sub-fractional Brownian motions with respective indices.
Assume. Our principal results are the necessary and sufficient condition for the
existence and smoothness of the collision local time and the intersection local time of
and through chaos expansion and elementary inequalities.     

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??How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

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There're about 10^{11} neurons in the human brain.Through the synaptic junction, neurons have formed a highly complex network.And it is really important to figure out the information expressed in the network, which will contribute to the resolution of the prevention and diagnosis of cognitive disorder of human beings. This paper uses the schizophrenia and healthy controlled subjects' fMRI data to construct the brain network model, in order to explores abnormal topological properties of schizophrenics' brain network based on graph theory. When studying the human brain network information traditionally by the basement of graph theory, it's all assure that the human brain network model has invariance, so it takes the whole period of time series data in constructing human networkmodel, which is a kind static network. However, it's hard to ensure this because of the nonstationarity of fMRI functional time series data. Thus, when constructing human brain network model, we should take its time-variation into consideration, then construct a dynamic brain network. We can explorethe brain network information better. In this research, we segment the time series data, using time windows, to constructing dynamic brain network model,then analyze it combined with the knowledge of graph theory, thereby reducing effects that the nonstationarity of fMRI functional time series data willhave. Comparing dynamic brain network of the schizophrenic patients with normal controls subjects' in different level, the results show that there are difference in single node property, group network property of schizophrenic patients and normal control subjects' whole brain dynamic functional connectivity network. The discovery of these difference in network topological properties has provide new clues for the further study on the pathological mechanism of schizophrenia.     

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In order to solve the problem of testing multidimensional diffusion models, we develop a test statistic based on Multi-Dimensional Tail Condition Expectations (CTEs). Although it is almost impossible to estimate the transition density matrix of a multidimensional diffusion model directly, the transition density of each component can be estimated and each component can be combined by the CTE to establish a true multidimensional statistics. Finally, the performance of the test is evaluated through simulation.     

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本文证明了copula , 生存copula ,对偶copula 和伴随copula 关于copula的复合运算构成一个四元群,给出了当某个单点值给定时它们的最优上下界. 计算了,时copula最优上下界的宽窄度,并与时的宽窄度进行了比较.