共查询到19条相似文献,搜索用时 93 毫秒
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刘再明 《数学年刊A辑(中文版)》1994,(6)
对于一般生灭矩阵Q(不必全稳定),文[1]解决了Q过程和不中断Q过程的存在性及唯一性问题.本文对含有限个瞬时态的生灭矩阵Q,构造了全部Q过程. 相似文献
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设Q为单瞬时态拟Q-矩阵,在本文中,我们给出了准B型Q过程存在的充要条件,特别,当Q为单瞬时准保守时,我们得到了Q为Q-矩阵的充要条件。 相似文献
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对于规则的Q矩阵,即Q保守且Q过程惟一时,证明了超规则Q过程的存在性.特别地,得到超Poisson过程、超规则生灭过程、超规则双边生灭过程、超规则纯生过程、超纯灭过程、超规则分支过程等的存在性. 相似文献
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张汉君 《数学年刊A辑(中文版)》1994,(3)
设E为可列集,Q=(qij;i,j∈E)为含瞬时态的拟Q-矩阵,且假定所有瞬时态均可和.在此假定下,本文得到如下三个结果:①准B型Q过程的存在准则.②Q为Q-矩阵的一个充分条件.③当Q准保守时,Q为Q-矩阵的充要条件.从而找到了瞬时态可和的准保守Q-矩阵的特征. 相似文献
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以首中时的矩来研究连续时间Markov链高阶偏差矩阵的存在及有限性, 并由此给出转移矩阵收敛到平稳分布的多项式速度的估计. 对于生灭过程, 给出了显式的表达式. 相似文献
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I. S. Kac 《Functional Analysis and Its Applications》2005,39(2):144-147
In a 1957 paper, Karlin and McGregor discovered the existence of birth-and-death processes for which the Chapman-Kolmogorov equation does not hold. Such processes are said to be pathological. We disclose the probability nature of pathological birth-and-death processes with the help of M. Krein’s spectral theory of strings.__________Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 74–78, 2005Original Russian Text Copyright © by I. S. Kac 相似文献
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The state 0 of a birth and death process with state space E = {0, 1, 2,....} is a barrier which can be classified into four kinds: reflection, absorption, leaping reflection, quasi-leaping reflection. For the first, second and fourth barriers, the characteristic numbers of different forms have been introduced. In this paper unified characteristic numbers for birth and death processes with barriers were introduced, the related equations were solved and the solutions were expressed by unified characteristic numbers. This paper concerns work solving probability construction problem of birth and death processes with leaping reflection barrier and quasi-leaping reflection barrier. 相似文献
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Jesper Møller 《Annals of the Institute of Statistical Mathematics》1989,41(3):565-581
Sufficient conditions for geometrical fast convergence of general spatial birth-and-death processes to equilibrium are established. 相似文献
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Fumiaki Machihara 《Operations Research Letters》1983,2(3):123-126
We analyze a class of finite dimensional birth-and-death processes. New conclusions are reached for the property of the eigenvalues of the infinitesimal generator for these processes. 相似文献
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We derive herein the limiting laws for certain stationary distributions of birth-and-death processes related to the classical model of chemical adsorption-desorption reactions due to Langmuir. The model has been recently considered in the context of a hybridization reaction on an oligonucleotide DNA-microarray. Our results imply that the truncated-gamma- and beta-type distributions can be used as approximations to the observed distributions of the fluorescence readings of the oligo-probes on a microarray. These findings might be useful in developing new model-based, probe-specific methods of extracting target concentrations from array fluorescence readings. 相似文献
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We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory in the diffusion setting by linking the separation distance in the primal diffusion to the absorption time in the dual diffusion. We also exhibit our strong stationary dual as the natural limiting process of the strong stationary dual sequence of a well-chosen sequence of approximating birth-and-death Markov chains, allowing for simultaneous numerical simulations of our primal and dual diffusion processes. Lastly, we show how our new definition of diffusion duality allows the spectral theory of cutoff phenomena to extend naturally from birth-and-death Markov chains to the present diffusion context. 相似文献
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研究含瞬时态、具有突变率的广义生-灭拟q-矩阵,在Q_(E_0)非零流出下,给出易于验证的Q过程存在性准则,并构造出全部Q过程和全部诚实Q过程,证明了不需附加任何条件,所有诚实Q过程都是遍历的,并求出其遍历测度以及给出诚实Q过程可配称的充要条件。最后给出两个例子以说明本文的结果易于验证。 相似文献
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A. B. Piunovskiy 《Mathematical Methods of Operations Research》2009,70(2):285-312
Fluid models are used to study functionals of the underlying random processes. Instead of analysing the trajectories, we investigate algebraic equations of the dynamic programming type which turn out to be discrete analogs of the corresponding differential equations. This analysis makes it possible to estimate the accuracy of approximation. Since the algebraic equations are the same for random walks and continuous time birth-and-death processes, we study the two cases in parallel. Several illustrative examples are also presented. 相似文献