On the first birth and the last death in a generation in a multi-type Markov branching process

In a multi-type continuous time Markov branching process the asymptotic distribution of the first birth in and the last death (extinction) of the kth generation can be determined from the asymptotic behavior of the probability generating function of the vector Z(^k)(t), the size of the kth generation at time t, as t tends to zero or as t tends to infinity, respectively. Apart from an appropriate transformation of the time scale, for a large initial population the generations emerge according to an independent sum of compound multi-dimensional Poisson processes and become extinct like a vector of independent reversed Poisson processes. In the first birth case the results also hold for a multi-type Bellman-Harris process if the life span distributions are differentiable at zero.     

Weak convergence in applied probability

Weak convergence of probability measures on function spaces has been active area of research in recent years. While the theory has a somewhat abstract base, it is extremely useful in a wide variety of problems and we believe has much to offer to applied probability. Our aim in this survey paper is to discuss those aspects of the theory which are relevant to work in applied probability. After an introduction to the foundations of weak convergence, we shall discuss partial sum, point, Markov and extremal processes. These processes form the building blocks for many of the important models of applied probability.     

Functional central limit theorems for a large network in which customers join the shortest of several queues

We consider N single server infinite buffer queues with service rate . Customers arrive at rate N, choose L queues uniformly, and join the shortest. We study the processes for large N, where R^N_t(k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We consider certain Hilbert spaces with the weak topology. First, we prove a functional central limit theorem (CLT) under the a priori assumption that the initial data R^N₀ satisfy the corresponding CLT. We use a compactness-uniqueness method, and the limit is characterized as an Ornstein-Uhlenbeck (OU) process. Then, we study the R^N in equilibrium under the stability condition <, and prove a functional CLT with limit the OU process in equilibrium. We use ergodicity and justify the inversion of limits lim _N lim _t= lim _t lim _N by a compactness-uniqueness method. We deduce a posteriori the CLT for R^N₀ under the invariant laws, an interesting result in its own right. The main tool for proving tightness of the implicitly defined invariant laws in the CLT scaling and ergodicity of the limit OU process is a global exponential stability result for the nonlinear dynamical system obtained in the functional LLN limit.Mathematics Subject Classification (2000):Primary: 60K35; Secondary: 60K25, 60B12, 60F05, 37C75, 37A30     

Evolution on a Smooth Landscape: The Role of Bias

The role of mutational bias in evolution on a smooth landscape is investigated. We consider both a finite-length genome where the bias increases linearly with the fitness, and an infinite genome with a fixed bias. We present simulations of finite populations in a waiting time model, showing both the nonequilibrium dynamics and the equilibrium fitness distributions that are reached. We compute the equilibrium analytically in several cases, using approximate direct solution of the master equations and truncated hierarchies.     

带负顾客和休假中止的Geo/Geo/1工作休假排队模型

将负顾客和休假中止策略引入离散时间休假排队.工作休假中当一个服务完成时有顾客等待则发生休假中止.负顾客作为一种干扰信号,文中规定其只在忙期中到达,负顾客不接受服务,一对一抵消队首正在接受服务的正顾客.利用拟生灭过程和矩阵几何解方法,得到了系统队长的稳态分布,也得到了稳态队长的条件随机分解结构.     

耶利内克戏剧《白雪公主》的互文性解析

《白雪公主》是奥地利女作家耶利内克的戏剧《死亡与少女》中的一部分,它与传统的格林童话在人物、情节和文字细节上形成互文性关系。但在主题上,它揭露并批判了女性潜在的奴性思想,同时又超越女性主义,直指人类终极命运——死亡。     

Siegmund Duality for Continuous Time Markov Chains on ℤ<Stack><Subscript>+</Subscript><Superscript>d</Superscript></Stack>

For the continuous time Markov chain with transition function P(t) on Z₊^d, we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P(t). If Q, the q-matrix of P(t), is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegmund dual of some Q-function is also given.     

吉林市2000～2005年孕产妇死亡率及死因分析

目的 通过对2000～2005年孕产妇死亡率及死因情况分析,分析孕产妇死亡的主要因素,提出干预措施.方法 回顾性分析的方法.结果 计算死亡率为42.81/10万.致死原因主要有产科出血和内科合并症.结论 加强产科管理,提高产科质量,降低孕产妇死亡率.     

Unified characteristic numbers and solutions of equations for birth and death processes with barriers

The state 0 of a birth and death process with state space E = {0, 1, 2,....} is a barrier which can be classified into four kinds： reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier.     

类克尔介质光腔中原子的纠缠动力学研究

初始处于纠缠的原子与附加类克尔介质的光腔相互作用,运用共生纠缠的度量方法对原子间的纠缠演化动力学进行研究,分析了腔场粒子数、介质非线性效应及原子与腔场的失谐量对纠缠演化的影响,发现处于腔场真空态下原子间的纠缠作周期性震荡演化,而处在腔场粒子数态下的原子在演化过程中发生纠缠突然死亡现象;在非线性克尔介质作用下,处于腔场粒子数较小范围内(n≤5)的原子间也会产生纠缠突然死亡现象;但随着腔场粒子数的增加纠缠突然死亡现象消失而且一定程度上可以达到纠缠初始值;当腔场处于任意粒子数态时,由于非线性效应的影响,均可抑制纠缠突然死亡现象的发生;当腔场在没有类克尔介质作用时,原子与腔场间的失谐量同样可以避免纠缠突然死亡现象的发生.