A Central Limit Theorem for Temporally Nonhomogenous Markov Chains with Applications to Dynamic Programming
成果类型：
Article
署名作者：
Arlotto, Alessandro; Steele, J. Michael
署名单位：
Duke University; University of Pennsylvania
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2016.0784
发表日期：
2016
页码：
1448-1468
关键词：
摘要：
We prove a central limit theorem for a class of additive processes that arise naturally in the theory of finite horizon Markov decision problems. The main theorem generalizes a classic result of Dobrushin for temporally nonhomogeneous Markov chains, and the principal innovation is that here the summands are permitted to depend on both the current state and a bounded number of future states of the chain. We show through several examples that this added flexibility gives one a direct path to asymptotic normality of the optimal total reward of finite horizon Markov decision problems. The same examples also explain why such results are not easily obtained by alternative Markovian techniques such as enlargement of the state space.
来源URL：