论文标题
在中央限制定理上的同质离散时间非线性马尔可夫链
On the central limit theorem for homogeneous discrete-time nonlinear Markov chains
论文作者
论文摘要
非线性马尔可夫过程的类别的特征是该过程的当前状态对当前分布的依赖性除了对先前状态的依赖性外。由于此特征，这些过程的特征是复杂的极限行为和厄贡特性，对此，马尔可夫过程的通常标准不够。作为非线性马尔可夫过程的子类，非线性马尔可夫链已经继承了这些功能。在本文中，研究了在离散时间和离散的有限状态空间中实现中央限制定理的中心限制定理的条件。此外，还包括对非线性马尔可夫链的厄法德特性的已知结果的简要回顾。所获得的结果补充了该领域的现有结果，对于统计数据的进一步应用可能很有用。
The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are characterized by complex limit behavior and ergodic properties, for which the usual criteria for Markov processes are not sufficient. Being a subclass of nonlinear Markov processes, nonlinear Markov chains have inherited these features. In this paper, conditions for the fulfillment of the central limit theorem for homogeneous nonlinear Markov chains in discrete time and with a discrete finite state space are studied. Also, a brief review of known results on the ergodic properties of nonlinear Markov chains is included. The obtained result complements the existing results in this area and may be useful for further applications in statistics.
