【作者】 李永奎；

【导师】 胡迪鹤；

【作者基本信息】 武汉大学 ， 概率论与数理统计， 2005， 硕士

【摘要】 本文是在Cogburn建立的随机环境中Markov链的数学模型的基础上,主要研究随机环境中可数Markov链的位势的几个相关问题。 首先,我们讨论了随机环境中离散Markov链的禁忌概率的基本分解公式,引入在禁忌集状态可达的概念,从而得到首先可达分布矩的一个结果。然后,给出随机调和函数,极端随机调和函数和必离集的概念,用必离集的概念研究随机调和函数、极端随机调和函数的性质,进而得到随机调和函数是常向量函数的一个充分条件。最后,我们研究了随机环境中可数Markov链的位势初步。首先引入随机位势函数的概念,给出随机位势函数的一个首要条件,进而讨论非负随机上调和函数的唯一分解性。更多还原

【Abstract】 This text is on the basis of mathematics model of Markov chain in random environment that Cogburn sets up, the several relevant problems potential of denumerable Markov chain in random environment are researched mainly.First of all, we discuss taboo probability of discrete Markov chain decomposition formulas basically in random environment, and introduce the concept that the state can be reached under the condition of the taboo set, a result of the moments of fist entrance time distributions is given. Moreover, provide the concepts of random harmonic functions, extreme harmonic function and inevitable exit set, some basic properties of them are studied by the concepts of inevitable exit sets, and then a sufficient condition for random harmonic functions to be the constant vector functions is obtained. Finally, the potential of denumerable Markov chain in random environment is preliminary that we have studied. Introduce the concept of random regular function and random potential function at first, a necessary and sufficient condition of random potential function for denumerable Markov chain in random environment is provided, and the unique decomposition property of nonnegative random super-regular function is discussed.更多还原