| 含瞬时态、具有突变率的广义生-灭Q-矩阵(I) |
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| 引用本文： | 吴群英,张汉君,侯振挺.含瞬时态、具有突变率的广义生-灭Q-矩阵(I)[J].数学年刊A辑(中文版),2003(2). |
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| 作者姓名： | 吴群英 张汉君 侯振挺 |
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| 作者单位： | 中南大学铁道校区科研所，中南大学铁道校区科研所，中南大学铁道校区科研所 长沙410075 桂林工学院数理系，广西桂林541004.，长沙410075，长沙410075 |
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| 基金项目： | 国家自然科学基金(No.19871006)，广西自然科学基金(No.桂科青9912008)资助的项目. |
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| 摘 要： | 研究含瞬时态、具有突变率的广义生-灭拟q-矩阵,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过程都是常返的,给出诚实Q过程是遍历的充要条件,并求出其遍历测度,以及证明了不存在可配称Q过程.最后给出两个例子以说明我们的结果易于验证.
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| 关 键 词： | 瞬时态 广义生-灭Q过程 构造定理 存在性 常返性 遍历性 |
AN EXTENDED BIRTH-DEATH Q-MATRIX WITH INSTANTANEOUS STATE AND CATASTROPHES (I) |
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| WU Qunying ZHANG Hanjun HOU Zhenting,Research.AN EXTENDED BIRTH-DEATH Q-MATRIX WITH INSTANTANEOUS STATE AND CATASTROPHES (I)[J].Chinese Annals of Mathematics,2003(2). |
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| Authors: | WU Qunying ZHANG Hanjun HOU Zhenting Research |
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| Institution: | WU Qunying ZHANG Hanjun HOU Zhenting
Research Department Railway Campus,Central South University,Changsha 410075,China and Department of Mathematics and Physics,Guilin Institute of Technology,Guilin 541004,Guangxi,China. E-mail: base@glite.edu.cn Research Department Railway Campus,Central South University,Changsha 410075,China. |
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| Abstract: | A new structure with the special property that instantaneous state and catastrophes is imposed to ordinary Birth-Death processes is considered. The authors give easy-checking existence criteria for such Markov processes. All the Q-processes and the honest Q-processes are explicitly constructed. Recurrent and ergodicity properties for the honest Q-processes are investigated. Surprisingly, it can be proved that all the honest Q-processes are recurrent without necessarily imposing any extra conditions. Ergodicity of such processes is also investigated and solved. Equilibrium distributions are then established. All the Q-processes are not symmetric. Two examples are provided to illustrate our results. |
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| Keywords: | Instantaneous state Extended birth-death Q-process Construction theorem Existence Recurrence Ergodicity |
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