马氏环境中可数马氏链的Poisson极限率

研究了马氏环境中的可数马氏链,主要证明了过程于小柱集上的回返次数是渐近地服从Poisson分布。为此,引入熵函数h,首先给出了马氏环境中马氏链的Shannon-Mc Millan-Breiman定理,还给出了一个非马氏过程Posson逼近的例子。当环境过程退化为一常数序列时,便得到可数马氏链的Poisson极限定理。这是有限马氏链Pitskel相应结果的拓广。     

一个强极限定理

设是可列非齐次马氏链，本文通过利用［１］中提出的在Ｗｉｅｎｅｒ概率空间的一种实现，而给出了一个对任意可列非齐次马氏链普遍成立的强极限定理。     

Moderate deviations for time-varying dynamic systems driven by non-homogeneous Markov chains with Two-time Scales

Motivated by problems arising in time-dependent queues and dynamic systems with random environment, this work develops moderate deviations principles for dynamic systems driven by a fast-varying non-homogeneous Markov chain in continuous time. A distinct feature is that the Markov chain is time dependent or inhomogeneous, so are the dynamic systems. Under irreducibility of the non-homogeneous Markov chain, moderate deviations of a non-homogeneous functional are established first. With the help of a martingale problem formulation and a functional central limit theorem for the two timescale system, both upper and lower bounds of moderate deviations are obtained for the rapidly fluctuating Markovian systems. Then applications to queueing systems and dynamic systems modulated by a fast-varying Markov chain are examined.     

马氏环境中马氏链的Poisson极限律

本文研究了马氏环境中马氏链,证明了该过程于小柱集上的回返次数是渐近地服从Poisson分布的,同时还给出了该过程是(?)-混合的一个充分条件以及过程回返于小柱集之概率的一个指数估计式.     

A Markov Renewal Based Model for Wireless Networks

We propose a queueing network model which can be used for the integration of the mobility and teletraffic aspects that are characteristic of wireless networks. In the general case, the model is an open network of infinite server queues where customers arrive according to a non-homogeneous Poisson process. The movement of a customer in the network is described by a Markov renewal process. Moreover, customers have attributes, such as a teletraffic state, that are driven by continuous time Markov chains and, therefore, change as they move through the network. We investigate the transient and limit number of customers in disjoint sets of nodes and attributes. These turn out to be independent Poisson random variables. We also calculate the covariances of the number of customers in two sets of nodes and attributes at different time epochs. Moreover, we conclude that the arrival process per attribute to a node is the sum of independent Poisson cluster processes and derive its univariate probability generating function. In addition, the arrival process to an outside node of the network is a non-homogeneous Poisson process. We illustrate the applications of the queueing network model and the results derived in a particular wireless network.     

非齐次树上非齐次马氏链的若干强大数定律

通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,给出了一类非齐次树上m重连续状态非齐次马氏链的若干强大数定律,推广了相关结果.     

一个随机偏差定理

设{Xn,n≥0}是可列非齐次马尔可夫链,Sn(i0,i1,…,im-1,ω)表示m元状态序组(i0,i1,…,im-1)在序列(X0,X1,…,Xm-1),(X1,X2,…,Xm),…,(Xn-1,Xn,…,Xn+m-2)中出现的次数.本文给出了关于Sn(i0,i1,…,im-1,ω)的一个对任意可列非齐次马尔可夫链普遍成立的随机偏差定理,即用不等式表示的一个强极限定理.     

Non-homogeneous space-time fractional Poisson processes

The space-time fractional Poisson process (STFPP), defined by Orsingher and Poilto (2012), is a generalization of the time fractional Poisson process (TFPP) and the space fractional Poisson process (SFPP). We study the fractional generalization of the non-homogeneous Poisson process and call it the non-homogeneous space-time fractional Poisson process (NHSTFPP). We compute their pmf and generating function and investigate the associated differential equation. The limit theorems for the NHSTFPP process are studied. We study the distributional properties, the asymptotic expansion of the correlation function of the non-homogeneous time fractional Poisson process (NHTFPP) and subsequently investigate the long-range dependence (LRD) property of a special NHTFPP. We investigate the limit theorem for the fractional non-homogeneous Poisson process (FNHPP) studied by Leonenko et al. (2014). Finally, we present some simulated sample paths of the NHSTFPP process.     

一个关于马尔可夫链的极限定理

给出一个关于可列非齐次马尔可夫链M元状态序组出现频率的新形式的强极限定理,所得结论对任意可列非齐次马尔可夫链普遍成立.     

非齐次树指标马氏双链转移矩阵的一个强极限性质

强极限定理是概率论中的重要问题之一.通过引入广义赌博系统的概念,研究给出了关于非齐次树指标马氏双链转移矩阵的一个强极限定理.     

关于极限定理的一个结果及其推广

给出了一个关于可列非齐次马尔可夫链M元状态序组出现频率的一个强极限定理及其推广,所得结论对任意可列非齐次马尔可夫链普遍成立.     

可列非齐次马氏链的一个强极限定理

本文提出可列非齐次马氏链关于状态出现频率的一个强权限定理．     

关于可列非齐次马尔可夫链的一个强极限定理及其推广

给出关于可列非齐次马尔可夫链M元状态序组出现频率的一个新形式的强极限定理及其推广,所得结论对任意可列非齐次马尔可夫链普遍成立.     

Central limit theorem for triangular arrays of non-homogeneous Markov chains

In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower bound estimate for the variance of partial sums. The results complement an important central limit theorem of Dobrushin based on the contraction coefficient.     

The statistics of words on rings

We analyze sequences of letters on a ring. Our objective is to determine the statistics of the occurrences of a set of r‐letter words when the sequence is chosen as a periodic Markov chain of order ≤ r ? 1. We first obtain a generating function for the associated probability distribution and then display its Poisson limit. For an i.i.d. letter sequence, correction terms to the Poisson limit are given. Finally, we indicate how a hidden Markov chain fits into this scheme. © 2005 Wiley Periodicals, Inc.     

一个随机偏差定理

设{Xn，n≥0}是可列非齐次马尔可夫链，Sn（i0，i1，…，im-1，ω）表示m元状态序组（i0，i1，…，im-1）在序列（X0，X1，…，Xm-1），（X1，X2，…，Xm），…，（Xn-1，Xn，…，Xn＋m-2）中出现的次数.本文给出了关于Sn（i0，i1，…，im-1，ω）的一个对任意可列非齐次马尔可夫链普遍成立的随机偏差定理，即用不等式表示的一个强极限定理.     

隐非齐次马尔可夫模型的强大数定律

本文研究了一类隐非齐次马尔可夫模型的强极限定理.利用鞅差序列收敛定理,获得了观测链{Y_n,n≥0}的强大数定律,并给出了观测链的Shannon-McMillan定理.     

非齐次树上马氏信源的一类Shannon-McMillan定理

通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,给出了非齐次树上m重非齐次马氏信源的一类Shannon-McMillan定理.     

非齐次树上k重非齐次马氏链的若干强偏差定理

通过引入样本散度的概念和构造辅助非负鞅,利用Doob鞅收敛定理研究给出了非齐次树上k重非齐次马氏链的若干强偏差定理.     

Bethe树和Cayley树上奇偶马尔可夫链场的强极限定理

本文介绍了N元Bethe树TB,N(N元Cayley树TC,N)上的奇偶马尔可夫链场的定义,并通过构造两个非负鞅证得了随机变量序列的强极限定理,应用此强极限定理获得了奇偶马尔可夫链场上的一个强极限定理,作为它的推论得到了状态和状态序偶出现频率的一类强极限定理及其估计,从而推广了关于N元Bethe树上马氏链场和二进树上奇偶马氏链场的部分强极限定理.