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摘要翻译：
本文研究了转移概率为完全连续算子核的马尔可夫链的时间平均行为，从而给出了动态经济模型中常用的一类马尔可夫链遍历的一个充分条件。本文讨论了拟弱完全连续马尔可夫算子收敛到唯一投影算子的时间平均收敛性。进一步的拟强完全连续性假设通过遍历分解降低了唯一不变测度对其初始分布的依赖，从而保证了Markov链在常系数乘法下是遍历的。并给出了外生随机冲击引起的经济状态马氏链遍历性的充分条件和状态空间与外生空间的对应关系。
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英文标题：
《Operator-Theoretical Treatment of Ergodic Theorem and Its Application to
Dynamic Models in Economics》
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作者：
Shizhou Xu
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最新提交年份：
2018
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Economics 经济学
二级分类：Theoretical Economics 理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
The purpose of this paper is to study the time average behavior of Markov chains with transition probabilities being kernels of completely continuous operators, and therefore to provide a sufficient condition for a class of Markov chains that are frequently used in dynamic economic models to be ergodic. The paper reviews the time average convergence of the quasi-weakly complete continuity Markov operators to a unique projection operator. Also, it shows that a further assumption of quasi-strongly complete continuity reduces the dependence of the unique invariant measure on its corresponding initial distribution through ergodic decomposition, and therefore guarantees the Markov chain to be ergodic up to multiplication of constant coefficients. Moreover, a sufficient and practical condition is provided for the ergodicity in economic state Markov chains that are induced by exogenous random shocks and a correspondence between the exogenous space and the state space.
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PDF链接：
https://arxiv.org/pdf/1811.06107
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