关于树指标m重非齐次马氏链的若干强偏差定理

强极限定理是概率论中的重要问题之一.强偏差定理是用不等式表示的一类强极限定理.本文通过构造非齐次树上的非负鞅,给出了关于树指标m重非齐次马尔科夫链的若干强偏差定理.     

一类非齐次树上的非齐次马尔可夫链的若干强极限定理

极限定理一直是国际概率论界研究的中心课题之一.通过构造适当的辅助非负鞅而给出了一类特殊非齐次树上可列状态的非齐次马尔可夫链场的若干强极限定理.     

M阶非齐次马氏链随机转移概率调和平均的一类强极限定理

主要研究任意m阶非齐次马氏链的随机转移概率调和平均的a.s.收敛的强极限定理.在证明中采用了一种把网微分法与条件矩母函数相结合应用于马氏链强极限定理研究的新途径.作为推论,得到m阶非齐次马氏链的一个公平比的强极限定理,并将已有的结果加以推广.     

树指标马氏链关于泊松分布的一个强极限定理

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.在概率论的发展过程中,对强极限定理的研究一直占重要地位,强极限定理也一直是国际概率论界研究的中心课题之一.本文通过引入滑动相对熵的概念和构造非负鞅,利用Doob鞅收敛定理研究给出了非齐次树指标马氏链关于泊松分布的一个强极限定理.     

非齐次树上m阶非齐次马氏连的一类强极限定理

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.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,研究给出了一类非齐次树上m阶非齐次马氏链的若干强极限定理.     

非齐次树上m重非齐次马氏链的若干强极限定理

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.研究给出了一类非齐次树上m重非齐次马氏链的若干强极限定理.     

m阶马氏链关于广义随机选择系统的极限定理

主要研究广义随机选择系统中的m阶非齐次马氏链随机转移概率调和平均的a.s.收敛的强极限定理.在证明中采用了一种把网微分法与条件矩母函数相结合应用于马氏链强极限定理研究的新途径.作为推论,得到m阶非齐次马氏链随机条件概率一个公平比的强极限定理,并将已有的结果加以推广.     

非齐次树上马氏双链的一个强极限定理

树指标随机过程已成为近年发展起来的概率论的研究方向之一.强极限定理一直是国际概率论界研究的中心课题之一.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,研究给出了一类非齐次树上马氏双链的一个强极限定理.     

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.     

关于极限定理的随机转移

<正> 许多作者([3]-[5])曾研究过随机变量序列的部分和极限定理的随机转移.D.J.Aldous在[1]中讨论了函数空间D[0,+∞)上一类较广泛的随机指标极限定理.本文考察有别于他们工作的一类函数型极限定理的随机转移;文中首先讨论函数空间D[0,1]上泛函正态极限定理的随机转移问题,接着讨论一些非正态随机极限定理.     

Central limit theorems for supercritical branching Markov processes

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems proved in [1] for branching OU processes with binary branching mechanisms. Compared with the results of [1], our central limit theorems are more satisfactory in the sense that the normal random variables in our theorems are non-degenerate.     

A universal result in almost sure central limit theory

The discovery of the almost sure central limit theorem (Brosamler, Math. Proc. Cambridge Philos. Soc. 104 (1988) 561–574; Schatte, Math. Nachr. 137 (1988) 249–256) revealed a new phenomenon in classical central limit theory and has led to an extensive literature in the past decade. In particular, a.s. central limit theorems and various related ‘logarithmic’ limit theorems have been obtained for several classes of independent and dependent random variables. In this paper we extend this theory and show that not only the central limit theorem, but every weak limit theorem for independent random variables, subject to minor technical conditions, has an analogous almost sure version. For many classical limit theorems this involves logarithmic averaging, as in the case of the CLT, but we need radically different averaging processes for ‘more sensitive’ limit theorems. Several examples of such a.s. limit theorems are discussed.     

B值随机变量序列的一类局部收敛定理

研究取值于Banach空间随机变量序列的一类局部收敛定理．作为推论,得到了一类B值鞅差序列的极限定理和经典的独立随机变量序列的极限定理,     

Limit theorems for random transformations and processes in random environments

I derive general relativized central limit theorems and laws of iterated logarithm for random transformations both via certain mixing assumptions and via the martingale differences approach. The results are applied to Markov chains in random environments, random subshifts of finite type, and random expanding in average transformations where I show that the conditions of the general theorems are satisfied and so the corresponding (fiberwise) central limit theorems and laws of iterated logarithm hold true in these cases. I consider also a continuous time version of such limit theorems for random suspensions which are continuous time random dynamical systems.

     

Limit theorems with refinements for random processes

One considers the problem of the derivation of limit theorems with refinements in functional spaces. One proves theorems on the expansions of the mathematical expectations of bounded continuous linear functionals of the trajectories of a Gaussian random process. From these theorems one derives a limit theorem with correction terms for the mathematical expectation of a functional of the trajectories of the time-discretized Wiener process, when the step of the discretization tends to zero. One discusses questions regarding generalizations, methods of proof, and the relation of these kind of limit theorems with other problems of the theory of probability, as well as possible applications of these theorems.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 94–114, 1986.     

关于任意随机序列的强收敛性

该文的目的是要研究任意随机序列的强极限定理。作为推论，得到了一类鞅差序列的强大数定律，一类随机序列公平比的强极限定理，以及任意随机序列部分和估计定理。      

树上路径过程的随机路径条件概率的强极限定理

本文研究了树上路径过程随机转移概率和状态序偶出现频率的强极限定理.通过利用若干重要不等式,获得了树上路径过程的随机路径条件概率用不等式表示的几何平均强极限定理以及树上路径过程关于状态序偶出现频率的用不等式表示的强极限定理,所得结果推广了树上马氏链及非齐次马氏链中的结果.     

一类适应随机变量序列的强极限定理

研究了一类适应随机变量序列的局部收敛性,推广了文献[1]中的结论.并在假定部分和序列为极限鞅时,得到了极限鞅的强极限定理.最后给出了*-mixing序列的强大数定律.     

The uniqueness of limit cycles for Liénard system

In monographs [Theory of Limit Cycles, 1984] and [Qualitative Theory of Differential Equations, 1985], eleven propositions by several mathematicians are listed on the uniqueness of limit cycles for equations of type (I), (II), and (III) of the quadratic ordinary differential systems. In this paper, we first point out that all these propositions were not completely proved since the equations under consideration do not satisfy the conditions of the theorems used to guarantee the uniqueness of limit cycles. Then we give a new set of theorems that guarantee the uniqueness of limit cycles for the Liénard systems, which not only can be applied to complete the proof of the propositions mentioned above but generalize many other uniqueness theorems as well. The conditions in these uniqueness theorems, which are independent and were obtained by different methods, can be combined into one improved general theorem that is easy to apply. Thus many of the most frequently used theorems on the uniqueness of limit cycles are corollaries of the results in this paper.