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本文研究了双无限环境中马氏链,构造了一马氏双链.利用马氏链的理论,在双链平稳遍历的条件下,获得了双无限环境中马氏链的中心极限定理成立的充分条件. 相似文献
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本文的目的 是要研究双无限随机环境下马氏链的一个强极限定理.作为推论得到了非齐次马氏链的一个强大数定律.最后,得到双无限随机环境中马氏链的随机转移概率调和平均的强极限定理. 相似文献
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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. 相似文献
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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. 相似文献
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马氏环境中马氏链的中心极限定理 总被引:1,自引:0,他引:1
讨论了具有离散参数的马氏环境中马氏链的中心极限定理, 并给出了加在链和过程样本函数上的充分条件\bd 同时深入研究了$R_{\theta}$\,-链, 得到马氏环境中马氏链的中心极限定理成立的三个充分条件. 相似文献
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设{Xn,n≥0}是一列非齐次马尔科夫链,{an,n≥0}是一列固定的非负整数序列.首先构造了一个带参数的广义似然比函数,然后利用Borel-Cantelli引理证明随机变量序列几乎处处收敛性,得到了关于可列非齐次马氏链序偶广义平均的若干极限定理,推广了已有的结果. 相似文献
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Shlomo Levental 《Probability Theory and Related Fields》1988,80(1):101-118
Summary We study uniform limit theorems for regenerative processes and get strong law of large numbers and central limit theorem of this type. Then we apply those results to Harris recurrent Markov chains based on some ideas of K. Athreya, P. Ney and E. Nummelin. 相似文献
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Thomas G. Kurtz 《Stochastic Processes and their Applications》1978,6(3):223-240
A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form where , the Y1 are independent Poisson processes, and N is a parameter with a natural interpretation (e.g. total population size or volume of a reacting solution).The corresponding deterministic model, satisfies Under very general conditions limN→∞XN(t)=X(t) a.s. The process XN(t) is compared to the diffusion processes given by and Under conditions satisfied by most of the applied probability models, it is shown that XN,ZN and V can be constructed on the same sample space in such a way that and 相似文献
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Lajos Horvath 《Probability Theory and Related Fields》1990,85(3):413-424
Summary The local time of a Markov process can be constructed from the length of small excursions. We obtain the exact almost sure rate of this construction. We also prove a functional limit theorem for the difference between the length of small excursions and the local time at zero. 相似文献
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David E. Handelman 《Journal d'Analyse Mathématique》1999,78(1):61-116
Associated to classes of countable discrete Markov chains or, more generally, column-finite nonnegative infinite matrices,
and a finite subset of the state space, is a dimension group. In many cases, this dimension group gives information about
the nonnegative eigenvectors of the process. Moreover, the study of the nonnegative eigenvectors is, equivalent to the traces
on an analytic one parameter family of dimension groups. We pay particular attention to the case that there is at most one
nonnegative eigenvector per eigenvalue, giving a number of sufficient conditions. Using the techniques developed here, we
also show that under a reasonable set of conditions (principle among them that there be just one nonnegative eigenvector for
the spectral radius), a (one-sided) ratio limit theorem holds.
Supported in part by an operating grant from NSERC (Canada) and an Isaac Walton Killam Fellowship (Canada Council). 相似文献
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Andrew D. Barbour 《Stochastic Processes and their Applications》1976,4(1):33-40
In a Markov branching process with random environments, limiting fluctuations of the population size arise from the changing environment, which causes random variation of the ‘deterministic’ population prediction, and from the stochastic wobble around this ‘deterministic’ mean, which is apparent in the ordinary Markov branching process. If the random environment is generated by a suitable stationary process, the first variation typically swamps the second kind. In this paper, environmental processes are considered which, in contrast, lead to sampling and environmental fluctuation of comparable magnitude. The method makes little use either of stationarity or of the branching property, and is amenable to some generalization away from the Markov branching process. 相似文献
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V. D. Konakov 《Journal of Mathematical Sciences》1987,38(6):2327-2335
One proves the uniform convergence of the densities of the finite-dimensional distributions of certain families of Markov chains to the densities of the finite-dimensional distributions of a nondegenerate diffusion process.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 277–292, 1986.The author is grateful to S. A. Molchanov for numerous useful discussions. 相似文献
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We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition
densities are proved.
Received: 28 August 1998 / Revised version: 6 September 1999 / Published online: 14 June 2000 相似文献