Inference on the variance and smoothing of the paths of diffusions

We give a hypothesis testing method to fit the diffusion coefficient σ of a d-dimensional stochastic differential equation on the basis of the observation of certain functionals of regularizations of the solution.     

关于马氏环境中马氏链的强极限定理的注

利用鞅收敛定理讨论马氏环境中马氏链的强收敛性,建立相应的强大数定律,使得已知的一系列结果为其特例.     

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.     

A Product Theorem for Markov Chains with Application to PF-Queueing Networks

Queueing networks in random environments represent more realistic models of computer and telecommunication systems than classical product form networks. This is due to the fact that network behaviour often depends on human activities which may vary according to daytime dependent behavioural patterns as well as physiological and mental indexes. In this paper we establish a product connection theorem for Markov chains which contains some corresponding results for spatial processes as well as for queueing networks in random environment as special cases. We demonstrate how our results can be applied to construct an adequate model for wireless networks with hook up capacity.     

On central limit theorems for shrunken random variables

We discuss Central Limit Theorems and absence of limiting distributions for shrunken random variables.

     

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．     

Ergodic Theorems and Ergodic Decomposition for Markov Chains

This paper considers Markov chains on a locally compact separable metricspace, which have an invariant probability measure but with no otherassumption on the transition kernel. Within this context, the limit providedby several ergodic theorems is explicitly identified in terms of the limitof the expected occupation measures. We also extend Yosidasergodic decomposition for Feller-like kernels to arbitrarykernels, and present ergodic results for empirical occupation measures, aswell as for additive-noise systems.     

一个关于任意可列非齐次马尔可夫链普遍成立的强极限定理(英文)

本文的目的是要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.     

Occupation times for countable Markov chains. II. Chains with continuous time

The results of part I are carried over to Markov chains with continuous time. As opposed to the case of chains with discrete time, one establishes the Markov property of the occupation time process for the simplest one-dimensional symmetric random walk with continuous time.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 130, pp. 56–64, 1983.     

关于马氏链强极限定理的一个新结论

本文的目的是要给出一个新形式的对任意可列非齐次马氏链普遍成立的强极限定理     

A Monte Carlo Estimation of the Entropy for Markov Chains

We introduce an estimate of the entropy of the marginal density p ^t of a (eventually inhomogeneous) Markov chain at time t≥1. This estimate is based on a double Monte Carlo integration over simulated i.i.d. copies of the Markov chain, whose transition density kernel is supposed to be known. The technique is extended to compute the external entropy , where the p ₁ ^t s are the successive marginal densities of another Markov process at time t. We prove, under mild conditions, weak consistency and asymptotic normality of both estimators. The strong consistency is also obtained under stronger assumptions. These estimators can be used to study by simulation the convergence of p ^t to its stationary distribution. Potential applications for this work are presented: (1) a diagnostic by simulation of the stability property of a Markovian dynamical system with respect to various initial conditions; (2) a study of the rate in the Central Limit Theorem for i.i.d. random variables. Simulated examples are provided as illustration.      

非齐次马氏链的中心极限定理

本文将针对非齐次马氏链的转移矩阵列在Ces`aro收敛意义下,利用鞅的中心极限定理证明一个不同于Dobrushin结果的非齐次马氏链的中心极限定理。     

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.     

A hybrid algorithm for the minimum bounding sphere problem

Two primal approaches, the shrinking approach and the dual approach, have been studied for the exact Minimum Bounding Sphere (MBS) problem. In this paper, we present a dual algorithm that uses the shrinking approach to solve subproblems. The experiments show our hybrid algorithm is faster than the dedicated shrinking algorithm and dual algorithm for solving the exact MBS problem in large point sets.     

绕积马氏链的中心极限定理

讨论了具有离散参数的绕积马氏链的中心极限定理,给出了加在过程样本函数上充分条件。得到了绕积马氏链的中心极限定理成立的充分条件.     

A note on discontinuous time changes of Markov processes

The “time change” of a Markov process via the inverse of a discontinuous additive functional A_t can be accomplished in two steps. First, perform a time change via the inverse of the strictly increasing discontinuous additive functional obtained by replacing the continuous part of A_t by t. The second step is an ordinary time change via the inverse of a continuous additive functional. Decomposing the time change in this way is useful in studying the time changed process.     

树指标马氏链的一个强极限定理

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.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马氏链的一个强极限定理.