拟对称Markov链泛函型中心极限定理

本文研究了一般的马尔可夫链特别是拟对称马尔可夫链．利用Lyons-Meyer-Zheng对称马尔可夫过程的鞅分解，建立了泛函型中心极限定理．推广到了一般平稳遍历马尔可夫过程。     

非齐次隐马尔可夫模型随机变换的若干强极限定理

利用鞅方法讨论了非齐次隐马尔可夫模型变换的强极限定理,作为特殊情形,将随机选择的概念拓展到非齐次隐马尔可夫模型中,得到了关于有限非齐次隐马尔可夫模型随机选择与随机公平比的若干极限定理.     

二重非齐次马氏链及其随机变换的若干强极限定理

利用鞅方法,给出二重非齐次马尔可夫链三元函数的几个强极限定理.作为特例,将赌博系统的随机变换概念推广到二重马氏链情形,得到二重马氏链随机选择与随机公平比的若干极限定理.     

B值L^p极限鞅的若干性质

本文在1≤p<∞的情形下讨论了取值于 Banach 空间的 L~p 极限鞅的收敛性质,给出了 L~p 极限鞅的 Riesz 分解,并用 L~p 极限鞅的收敛性刻划了空间的 Radon-Nikodym 性质,从而把在 p=1情形下的一些结果推广到了1≤p<∞的情形。此外,还指出了 B 值 p 拟鞅,B 值 p 一致渐近鞅与本文中的 B 值 L~p 极限鞅之间的包含关系。     

集值 Pramart 的鞅分解

研究了集值Pramart的若干性质,利用支撑函数得到了集值Pramart的收敛定理,同时,证明了实值Pramart的鞅分解定理.以此为基础,给出了集值Pramart在Kuratowski-Mosco意义下的鞅分解定理.     

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.     

非对称马氏过程上穿估计和胎紧性

应用马尔可夫过程向前向后鞅分解方法, 将Lyons-Zheng的平均上穿次数估计由对称马尔可夫过程情形推广到非对称情形, 由此得到Meyer-Zheng拓朴的紧性判别准则,并用一个具体例子说明如何估计关键的上穿次数.     

广义Bethe树指标可列马氏链场关于广义随机选择系统的一类局部极限定理

研究任意广义Bethe树指标马尔可夫链场二元泛函关于广义随机选择系统的一类局部极限定理.作为推论得到了广义随机选择系统中任意Cayley树上状态频率和状态序偶的一类极限定理.证明中采用了一种研究马尔可夫链场的较新颖的分析方法.     

拟对称马尔可夫过程穿越次数估计

本文研究了马尔可夫过程穿越次数估计问题.利用向前向后鞅分解方法,获得了拟对称马尔可夫过程的穿越次数估计,将Lyons-Zheng的马尔可夫过程的穿越次数估计从对称情形推广到拟对称情形.     

定向集上的B值一致渐近鞅

本文将文献[1]、[2]关于序列情形下的B值一致渐近的概念拓广到定向集的情形,给出了定向集上B值鞅的一个可选采样定理,证明了定向集上B值一致渐近鞅的Riesz分解定理。同时,用B值一致渐近鞅的收敛性及其诱导测度刻划了B空间的R-N性质,最后还给出了一个B值一致渐近鞅本性收敛的充分条件。     

HILBERTIAN INVARIANCE PRINCIPLE FOR EMPIRICAL PROCESS ASSOCIATED WITH A MARKOV PROCESS

The authors establish the Hilbertian invariance principle for the empirical process of a stationary Markov process, by extending the forward-backward martingale decomposition of Lyons-Meyer-Zheng to the Hilbert space valued additive functionals associated with general non-reversible Markov processes.     

Stochastic integration for operator valued processes on hilbert spaces and on nuclear spaces

The representation of a nuclear space valued square integrable martingale by means of another nuclear space valued square integrable martingale is given in terms of stochastic inegrals of operator valued processes. The construction of the stochastic integral goes through that of operator valued processes on Hilbert spaces. A new approach is given for the Hilbertian case, so that only the integration of Hilbert-Schmidt operator valued processes is needed to represent square integrable martingales     

Banach空间值鞅不等式与弱大数定律

本文证明了Ｂａｎａｃｈ空间值鞅的一些不等式，讨论了Ｂａｎａｃｈ空间的凸性及光滑性与某些鞅不等的式的联系，给出了Ｈｉｌｂｅｒｔ空间的一个鞅不等式刻划，同时还讨论了一致Ｐ光滑空间中鞅的弱大数定律，本文的结论推广与改进了很多熟知的定理。     

Functional law of iterated logarithm for additive functionals of reversible Markov processes

1.IntroductionandMainResultsAssumethat(Xt),.T(T~NorAl)isaPolishspaceE-valuedMarkovprocess,definedon(fi,F,(R),(ot),(P-c)..E),withitssemigroupoftransitionkernels(Pt).Here(ot)isthesemigroupofshiftsonfisuchthatX.(otw)~X. t(w),Vs,tET;(R)isthenaturalfiltration.Throughoutthispaperweassumethat(Pt)issymmetricandergodicwithrespectto(w.r.t.forshort)aprobabilitymeasurepon(E,e)(eistheBorela--fieldofE),i.e.,.Symmetry:(Ptf,g)~(f,Pig):~isfptgdp,acET,if,gCL'(P);.ErgodicitytFOranyfEL'(P),ifPtf~f…     

Weak convergence to a Markov process: The martingale approach

Summary In this article, we obtain some sufficient conditions for weak convergence of a sequence of processes {X _n } toX, whenX arises as a solution to a well posed martingale problem. These conditions are tailored for application to the case when the state space for the processesX _n ,X is infinite dimensional. The usefulness of these conditions is illustrated by deriving Donsker's invariance principle for Hilbert space valued random variables. Also, continuous dependence of Hilbert space valued diffusions on diffusion and drift coefficients is proved.Research supported by National Board for Higher Mathematics, Bombay, IndiaPart of the work was done at University of California, Santa Barbara, USA     

Weak convergence of hilbert valued martingale measures

In this paper, we discuss the property of Hilbert valued martingale measure and introduce the concept of convergence of martingale measures in distribution. The sufficient. and necessary conditions are provided for strongly orthogonal martingale measures with independent increments (Theorem 2.2). The conditions are given for convergence of martingale measures     

On the Central Limit Theorem and Its Weak Invariance Principle for Strongly Mixing Sequences with Values in a Hilbert Space via Martingale Approximation

In this paper we not only prove an extension to Hilbert spaces of a sharp central limit theorem for strongly real-valued mixing sequences, but also slightly improve it. The proof is mainly based on the Bernstein blocking technique and approximations by martingale differences. Moreover, we derive also the corresponding functional central limit theorem.     

马尔可夫过程穿越次数估计

本文研究了马尔可夫过程穿越次数估计.应用马尔可夫过程向前向后鞅分解方法,得到了穿越次数估计以及Meyer-Zheng拓朴的紧性判别准则,推广了Lyons-Zheng的结果.     

Relatively optimal filtering on a Hilbert space for measure driven stochastic systems

In this paper we consider linear filtering for discontinuous processes determined by stochastic differential equations on a Hilbert space driven by signed measures in addition to Brownian motion. The dynamics of the observed data is governed by a differential equation driven by a square integrable martingale (not necessarily continuous) while perturbed by a signed measure. We formulate the filtering problem as an optimization problem on the space of bounded linear operator valued functions and present necessary and sufficient conditions for optimality. Further, we prove, under the assumption of finite dimensionality of the output space, that a Kalman-like filter exists and it is explicitly determined by a Riccati type evolution equation.