论文标题
求解泊松方程：存在，独特性，martingale结构和CLT
Solving Poisson's Equation: Existence, Uniqueness, Martingale Structure, and CLT
论文作者
论文摘要
泊松方程的解在构造马尔丁加尔的构造中起关键作用，可以分析马尔可夫相关的随机变量的总和。在本文中，我们研究了在可数的状态空间中解决方案的两种不同表示，一个基于再生结构，另一个基于无限期望值。我们还考虑了与泊松方程解决方案相关的集成性和相关唯一性问题，并提供可验证的Lyapunov条件以支持我们的理论。我们的关键结果包括在Lyapunov条件下比文献中出现的较弱的Lyapunov条件下的迭代对数定理和迭代对数定律。
The solution of Poisson's equation plays a key role in constructing the martingale through which sums of Markov correlated random variables can be analyzed. In this paper, we study two different representations for the solution in countable state space, one based on regenerative structure and the other based on an infinite sum of expectations. We also consider integrability and related uniqueness issues associated with solutions to Poisson's equation, and provide verifiable Lyapunov conditions to support our theory. Our key results include a central limit theorem and law of the iterated logarithm for Markov dependent sums, under Lyapunov conditions weaker than have previously appeared in the literature.
