随机环境中双移民生灭过程的极限性质

引入了随机环境中双移民生灭过程的概念，定义了过程的模态指示函数，在此基础上研究了其转移矩阵的平稳分布，给出了平稳分布众数的位置与模态指示函数之间的关系．研究了平稳分布的众数与边界关系．     

Random Classical Fidelity

We introduce a random perturbed version of the classical fidelity and we show that it converges with the same rate of decay of correlations, but not uniformly in the noise. This makes the classical fidelity unstable in the zero-noise limit.     

Moderate Deviations for Longest Increasing Subsequences: The Lower Tail

We derive a moderate deviation principle for the lower tail probabilities of the length of a longest increasing subsequence in a random permutation. It refers to the regime between the lower tail large deviation regime and the central limit regime. The present article together with the upper tail moderate deviation principle in Ref. 12 yields a complete picture for the whole moderate deviation regime. Other than in Ref. 12, we can directly apply estimates by Baik, Deift, and Johansson, who obtained a (non-standard) Central Limit Theorem for the same quantity.     

One-dimensional non-nearest-neighbor random walks in the presence of traps

A one-dimensional lattice random walk in the presence ofm equally spaced traps is considered. The step length distribution is a symmetric exponential. An explicit analytic expression is obtained for the probability that the random walk will be trapped at thejth trapping site.     

平面上随机级数的性质

研究了平面上系数{Xn,n≥0}为(?)-混合序列在满足,(q>1)等条件下的随机级数的增长性及值分布,得到了比较好的结果．     

Bayesian Prediction Analysis for Growth Curve Model Using Noninformative Priors

We apply a Bayesian approach to the problem of prediction in an unbalanced growth curve model using noninformative priors. Due to the complexity of the model, no analytic forms of the predictive densities are available. We propose both approximations and a prediction-oriented Metropolis-Hastings sampling algorithm for two types of prediction, namely the prediction of future observations for a new subject and the prediction of future values for a partially observed subject. They are illustrated and compared through real data and simulation studies. Two of the approximations compare favorably with the approximation in Fearn (1975, Biometrika, 62, 89–100) and are very comparable to the more accurate Rao-Blackwellization from Metropolis-Hastings sampling algorithm.     

Phase Transition in Vertex-Reinforced Random Walks on {\mathbb{Z}} with Non-linear Reinforcement

Vertex-reinforced random walk is a random process which visits a site with probability proportional to the weight w _k of the number k of previous visits. We show that if w _k ∼ k ^α, then there is a large time T ₀ such that after T ₀ the walk visits 2, 5, or ∞ sites when α < 1, = 1, or > 1, respectively. More general results are also proven.      

Semiconvergence in distribution of random closed sets with application to random optimization problems

The paper considers upper semicontinuous behavior in distribution of sequences of random closed sets. Semiconvergence in distribution will be described via convergence in distribution of random variables with values in a suitable topological space. Convergence statements for suitable functions of random sets are proved and the results are employed to derive stability statements for random optimization problems where the objective function and the constraint set are approximated simultaneously. The author is grateful to two anonymous referees for helpful suggestions.     

随机环境中多物种分枝随机游动

引进了随机环境中多物种分枝随机游动的一般模型.在分枝过程非灭绝的情况下,讨论了系统的状态分类,得到了系统暂留及强常返的充要条件是存在k个定义在整数集上的函数分别满足某种性质.最后给出了系统强暂留的充分条件.