Central Limit Theorems for Stochastic Approximation with controlled Markov chain dynamics
Central Limit Theorems for Stochastic Approximation with controlled Markov chain dynamics
复制标题
受控马尔可夫链动力学随机逼近的中心极限定理
DOI：
10.1051/ps/2014013
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
G. Fort
中科院分区：
文献类型：
--
作者：
G. Fort
本文给出了满足随机逼近方程$\theta_{n+1} = \theta_{n +1} H（\theta_{n，X_{n +1}）$的过程$\theta_n，n\geq 0\}$的中心极限定理（CLT），并建立了相应平均序列的中心极限定理.本文的独创性在于解决受控马尔可夫链动态$\{X_n，n\geq 0 \}$的情况和多目标的情况。该框架还容纳（随机）截断SA算法。充分条件CLT的举行，以及评论这些条件如何扩展以前的作品（如独立和同分布的动态，罗宾斯-门罗动态或单目标的情况下）。本文特别强调了这些条件如何适用于受控马尔可夫链动态和多目标的SA，证明了本文改进了现有的工作。
This paper provides a Central Limit Theorem (CLT) for a process $\{\theta_n, n\geq 0\}$ satisfying a stochastic approximation (SA) equation of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H(\theta_n,X_{n+1})$; a CLT for the associated average sequence is also established. The originality of this paper is to address the case of controlled Markov chain dynamics $\{X_n, n\geq 0 \}$ and the case of multiple targets. The framework also accomodates (randomly) truncated SA algorithms. Sufficient conditions for CLT's to hold are provided as well as comments on how these conditions extend previous works (such as independent and identically distributed dynamics, the Robbins-Monro dynamic or the single target case). The paper gives a special emphasis on how these conditions hold for SA with controlled Markov chain dynamics and multiple targets; it is proved that this paper improves on existing works.
影响因子：
1
作者：
Andrieu C
通讯作者：
Andrieu C