隐Markov模型的强马氏性

引入隐Markov模型强马氏性的概念,并进一步研究了隐Markov模型在强马氏性方面的一些性质.     

马氏模型下移动自组网随选型路由协议特性分析

移动自组网络（简称MANET）因其移动性及无基础设施支持等特点已经成为无线通信网络中的热门问题．通过将一个MANET网络中每条链边的长度看作一个生灭过程,并且假设在泛洪过程中空间可以复用n次,建立了移动自组网络空间可复用的马氏模型,简记为n-SRBDM．在一个典型的随选型路由协议即动态源路由（DSR）协议的基础上,研究了网络的一些关键性能参数,给出了路由泛洪距离的概率分布和期望,限定泛洪步数时成功寻路的概率、发现τ-时有效路径及对称有效路径的概率,发现一条有效路径的平均时间等,对于路由维护过程,也引入并研究了一些网络性能参数,例如,路由恢复的平均频率,路由有效的平均时间．对于这些网络参数在空间可复用和空间不可复用两种情形下进行了比较．证明了空间可复用模型下的路由选择更为有效．     

移动自组网络N次空间重用的离散时间马氏链模型

移动自组网络(简称MANET)目前已经成为4G中的重要研究课题.本文在一个典型的随选型路由协议即动态源路由(DSR)协议的基础上,通过对信号强度进行分级来描述节点之间的相对距离,同时利用定向天线技术,建立了移动自组网络有空间重用的离散时间马氏链模型.通过计算平稳分布,进一步分析了节点相邻的概率和节点的平均邻居数两个基本的网络参数.并以定向天线发送信号的特性为基础,给出了一个具体实例,分析相应的参数.这对路由协议的评价和性能分析具有理论上的指导意义.     

具有马氏调制的风险模型的均值-方差组合选择问题

本文研究了保险市场上的均值-方差组合选择问题.本文利用线性二次控制理论,得到了最优策略和有效的均值-方差边界的显示解.     

常数红利边界下的一类马氏风险模型

本文研究了常数红利边界下一类马氏风险模型的红利派发矩,破产前所有红利的分布等相关问题.利用更新方法,给出了该模型破产前红利折现的期望满足的微分-积分方程,得到破产前所有红利的分布.通过构造特殊的初始条件,得到了相关的方程组解,推广了文献[3]的结果.     

一类非齐次马氏链的绝对平均强遍历性

引用马氏链绝对平均强遍历的概念,首先给出齐次马氏链绝对平均强遍历与强遍历的等价性,其次通过引进另一个强遍历的非齐次马氏链,给出一个非齐次马氏链绝对平均强遍历的充分条件.     

一类索赔为马氏链的风险模型

本文研究了索赔为马氏链的离散风险模型.利用鞅方法得到破产概率的Lundberg不等式,并且给出了当索赔为独立同分布时的Lundberg不等式.     

马氏环境复合二项模型的条件概率计算北大核心CSCD

肖临在Cossette(2004)的基础上改进并建立了马氏链环境中复合二项风险模型,针对Cossette(2004)中所提出的几个命题在肖临的模型框架下给出了详细的证明,得出了有限时间的条件非破产概率递推公式及赔付额的条件概率函数的递推公式.     

一类最优投资随机控制模型的马氏链算法

现代金融经济中的很多问题可以构建成随机控制模型,而随机控制的求解却存在一定的困难.马氏链算法应该是一种有效的求解随机控制问题的数值方法.本文以Claus Munk的工作为基础,针对一类最优投资模型,具体确定了马氏链的转移矩阵并证明其满足算法收敛条件,并用MATLAB语言编成一个程序实现.     

树上非齐次马氏链随机转移概率的极限性质

收稿研究树上非齐次马氏链随机转移概率的调和平均极限性质,所得结果将非齐次马氏链上随机转移概率调和平均性质推广到树图上.     

Performance Analysis for Mobile Ad Hoc Network in Random Graph Models with Spatial Reuse

In this paper,we present a random graph model with spatial reuse for a mobile ad hoc network(MANET) based on the dynamic source routing protocol.Many important performance parameters of theMANET are obtained,such as the average flooding distance (AFD),the probability generating function of theflooding distance,and the probability of a flooding route to be symmetric.Compared with the random graphmodel without spatial reuse,this model is much more effective because it has a smaller value of AFD and alarger probability for finding a symmetric valid route.     

Stochastic Second-Order Cone Programming in Mobile Ad Hoc Networks

We propose a two-stage stochastic second-order cone programming formulation of the semidefinite stochastic location-aided routing (SLAR) model, described in Ariyawansa and Zhu (Q. J. Oper. Res. 4(3), 239–253, 2006). The aim is to provide a sender node S with an algorithm for optimally determining a region that is expected to contain a destination node D (the expected zone). The movements of the destination node are represented by ellipsoid scenarios, randomly generated by uniform and normal distributions in a neighborhood of the starting position of the destination node. By using a second-order cone model, we are able to solve problems with a much larger number of scenarios (20250) than it is possible with the semidefinite model (500). The use of a larger number of scenarios allows for the computation of a new expected zone, that may be very effective in practical applications, and for obtaining stability results for the optimal first-stage solutions and the optimal cost function values.     

Ad Hoc网络中的区域划分和资源分配问题

建立了Ad Hoc网络中的区域划分和资源分配的模型,重点对网络的最少小区数覆盖、抗毁性、节点分簇等问题进行了研究,并对节能性、通信质量评估进行了初步探讨.     

Ad Hoc网络中基于时分的分布式QoS路由算法

捷径冲突是AdHvc网络中QoS路由特有的一种现象，它由WenjianShao在[2]中首次提出．本文进一步研究了捷径冲突现象，给出了一个更加准确的定义，且给出了一个基于时分的分布式QoS路由算法成功地避免了捷径冲突现象．本算法是基于TDMA的分布式算法，每个节点只需了解网络的局部信息即可．数据分析表明本算法预留的最大带宽比较接近AdHoc网络中所能用的最大带宽．     

Ad Hoc网络区域划分和资源分配问题研究

主要利用图论、概率统计及优化理论对Ad-Hoc网络进行了数学建模.研究了等圆(不等圆)区域覆盖、带障碍区域的覆盖、确定性点覆盖、信道分配、抗毁度、节能性和通信质量等问题.定义了覆盖效率、抗毁性概率指标、覆盖系数、期望覆盖系数、网络寿命等一系列评价系数和衡量标准,提出了基于单位距离覆盖系数和期望覆盖系数的启发式寻优算法,并编程加以实现,得到较满意的近似解.     

Computational Bayesian Analysis of Hidden Markov Models

Abstract

Versions of the Gibbs Sampler are derived for the analysis of data from hidden Markov chains and hidden Markov random fields. The principal new development is to use the pseudolikelihood function associated with the underlying Markov process in place of the likelihood, which is intractable in the case of a Markov random field, in the simulation step for the parameters in the Markov process. Theoretical aspects are discussed and a numerical study is reported.     

Moments’ Analysis in Homogeneous Markov Reward Models

We analyze the moments of the accumulated reward over the interval (0,t) in a continuous-time Markov chain. We develop a numerical procedure to compute efficiently the normalized moments using the uniformization technique. Our algorithm involves auxiliary quantities whose convergence is analyzed, and for which we provide a probabilistic interpretation.     

Averaging in Markov Models with Fast Markov Switches and Applications to Queueing Models

An approximation of Markov type queueing models with fast Markov switches by Markov models with averaged transition rates is studied. First, an averaging principle for two-component Markov process (x _n (t), _n (t)) is proved in the following form: if a component x _n () has fast switches, then under some asymptotic mixing conditions the component _n () weakly converges in Skorokhod space to a Markov process with transition rates averaged by some stationary measures constructed by x _n (). The convergence of a stationary distribution of (x _n (), _n ()) is studied as well. The approximation of state-dependent queueing systems of the type M _M,Q /M _M,Q /m/N with fast Markov switches is considered.