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生灭型半马氏骨架过程 总被引:1,自引:0,他引:1
本文首先引进了生灭型半马氏骨架过程的定义,求出了两骨架时跳跃点τn-1(ω)与τn(ω)之间的嵌入过程X(n)(t,ω)的初始分布及寿命分布.得到了生灭型半马氏骨架过程的一维分布.其次引进了生灭型半马氏骨架过程的数字特征并讨论了它们的概率意义及相互关系.讨论了生灭型半马氏骨架过程的向上和向下的积分型随机泛函.最后讨论了它的遍历性及平稳分布,求出了平均首达时间及平均返回时间.得到了常返和正常返的充分必要条件,求出了在正常返的条件下的平稳分布. 相似文献
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广生灭过程的遍历性及平稳分布 总被引:1,自引:0,他引:1
文献[1]研究了广生灭过程的向上积分型随机泛函,得到了广生灭过程的若干数字特征以及常返的充要条件,该文讨论广生灭过程向下积分型随机泛函,给出了广生灭过程遍历的充要条件以及平均返回时间的计算公式,并在遍历的条件下求出了广生灭过程的平稳分布. 相似文献
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本文提出了一个项目参与者数T是随机变量的广义合作网络模型,新节点与随机选择的节点合作,通过节点度演化所满足的马尔可夫性,利用马.尔可夫链的方法和技巧得到了度分布的精确解析表达式.并说,明了此广义合作网络不是无标度网络. 相似文献
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《Stochastic Processes and their Applications》2020,130(2):878-906
Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree distributions, not much investigation has been done on the joint behavior of the in- and out-degree growth. Also, statistical estimates of the marginal tail exponent of the power-law degree distribution often use the Hill estimator as one of the key summary statistics, even though no theoretical justification has been given. This paper focuses on the convergence of the joint empirical measure for in- and out-degrees and proves the consistency of the Hill estimator. To do this, we first derive the asymptotic behavior of the joint degree sequences by embedding the in- and out-degrees of a fixed node into a pair of switched birth processes with immigration and then establish the convergence of the joint tail empirical measure. From these steps, the consistency of the Hill estimators is obtained. 相似文献
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The three node Jackson queueing network is the simplest acyclic network in which in equilibrium the sojourn times of a customer at each of the nodes are dependent. We show that assuming the individual sojourn times are independent provides a good approximation to the total sojourn time. This is done by simulating the network and showing that the sojourn times generally pass a Kolmogorov-Smirnov test as having come from the approximating distribution. Since the sum of dependent random variables may have the same distribution as the sum of independent random variables with the same marginal distributions, it is conceivable that our approximation is exact. However, we numerically compute upper and lower bounds for the distribution of the total sojourn time; these bounds are so close that the approximating distribution lies outside of the bounds. Thus, the bounds are accurate enough to distinguish between the two distributions even though the Kolmogorov-Smirnov test generally cannot. 相似文献
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Zhixin Sun Yuhua XuJing Gong Zhiguang Ren 《Applied mathematics and computation》2011,218(7):3723-3732
Aiming at constructing a delay and delay variation bounded Steiner tree in the real-time streaming media communication, in this paper, we discuss a multicast routing algorithm based on searching a directed graph (MRASDH). During the process of the construction of the multicast tree, some nodes and links in the network topology do not affect the outcome of the constructed tree. Therefore, based on the thought of shrinking the search space through deleting these non-relative nodes and edges to the utmost, the ant algorithm is utilized to generate a directed sub-graph of the network topology for each destination node, in which each node owns a bounded out-degree. And all these sub-graphs can be merged into a new directed graph that serves as the new search space. In the new space, the simulated annealing algorithm is applied to obtain a multicast tree that satisfies the condition for the optimization. The performance analysis and simulation results demonstrate that this algorithm can effectively construct a delay and delay variation bounded multicast tree. They also show that the algorithm have lower time complexity than the current ones, which means a much better result would be achieved when the system scale rises greatly. 相似文献
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王振宇 《数学物理学报(A辑)》2010,30(5):1248-1253
在并发程序复杂性度量研究中, 作者曾定义了所谓B图, 用以作为 Ada 并发程序中一种会合关系的模型. 该文研究B 图的一种特殊情况---BB图, 一类链状图.n节点 BB 图是在n个节点、高为n-1的有向树上再添加若干条边,其约束条件是: 每个节点的入度不大于二, 每个节点的出度也不大于二. 该文给出BB 图图的若干若干枚举特征,并指出这些特征同第二类Stirling数的密切关系. 相似文献
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The Gibbs sampler is a popular Markov chain Monte Carlo routine for generating random variates from distributions otherwise difficult to sample. A number of implementations are available for running a Gibbs sampler varying in the order through which the full conditional distributions used by the Gibbs sampler are cycled or visited. A common, and in fact the original, implementation is the random scan strategy, whereby the full conditional distributions are updated in a randomly selected order each iteration. In this paper, we introduce a random scan Gibbs sampler which adaptively updates the selection probabilities or “learns” from all previous random variates generated during the Gibbs sampling. In the process, we outline a number of variations on the random scan Gibbs sampler which allows the practitioner many choices for setting the selection probabilities and prove convergence of the induced (Markov) chain to the stationary distribution of interest. Though we emphasize flexibility in user choice and specification of these random scan algorithms, we present a minimax random scan which determines the selection probabilities through decision theoretic considerations on the precision of estimators of interest. We illustrate and apply the results presented by using the adaptive random scan Gibbs sampler developed to sample from multivariate Gaussian target distributions, to automate samplers for posterior simulation under Dirichlet process mixture models, and to fit mixtures of distributions. 相似文献
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Hosam M. Mahmoud 《Methodology and Computing in Applied Probability》2010,12(4):763-773
The power of choice is known to change the character of random structures and produce desirable optimization effects. We discuss
generalizations of random recursive trees, grown under the choice to meet optimization criteria. Specifically, we discuss
the random k-minimal (k-maximal) label recursive tree, where a set of k candidate parents, instead of one as in the usual recursive tree, is selected and the node with minimal (maximal) label among
them is assigned as parent for the next node. These models are proposed as alternatives for D’Souza et al. (Eur Phys J B59:535–543,
2007) minimal and maximal depth models. The advantage of the label models is that they are tractable and at the same time provide
approximations and bounds for the depth models. For the depth of nodes in label models we give the average behavior and exact
distributions involving Stirling’s numbers and derive Gaussian limit laws. 相似文献
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Masaaki Sibuya 《Annals of the Institute of Statistical Mathematics》1993,45(3):459-465
A clustering process which generates simple and uniform random partitions is studied. It has a single parameter and generates, for a special value of the parameter, the partition of a random permutation into its cycles. The limit distribution of the size index of the generated partition is the joint of the independent Poisson distributions with means determined by the size and the parameter. 相似文献
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Shankar Bhamidi Amarjit Budhiraja Ruoyu Wu 《Stochastic Processes and their Applications》2019,129(6):2174-2206
We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The collection of neighbors of a given node changes dynamically over time and is determined through a time evolving random graph process. A law of large numbers and a propagation of chaos result is established for a multi-type population setting where at each instant the interaction between nodes is given by an inhomogeneous random graph which may change over time. This result covers the setting in which the edge probabilities between any two nodes are allowed to decay to 0 as the size of the system grows. A central limit theorem is established for the single-type population case under stronger conditions on the edge probability function. 相似文献
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K. Jayakumar 《Mathematical and Computer Modelling》2003,37(12-13):1427-1434
First-order autoregressive Mittag-Leffler process is studied. Methods for generating dependent (first-order autoregressive Markovian) sequences of random variables with Mittag-Leffier marginal distributions are discussed. Comparison of the first-order autoregressive Mittag-Leffler process with the first-order autoregressive exponential process of Gaver and Lewis [1] is done. As an application, the first-order autoregressive Mittag-Leffier process is fitted to weakly stream flows of the Kallada River in Kerala, India. 相似文献
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SOMEMULTIVARIATEDMRLANDNBUEDEFINITIONSBASEDONCONDITIONALSTOCHASTICORDERWANGYUEDONG(王跃东)CAOJINHUA(曹晋华)(DepartmentofStatistics,... 相似文献