Applications of a Kushner and Clark lemma to general classes of stochastic algorithms
Applications of a Kushner and Clark lemma to general classes of stochastic algorithms
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库什纳和克拉克引理在一般类随机算法中的应用
DOI：
10.1109/tit.1984.1056894
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
P. Priouret
中科院分区：
文献类型：
--
作者：
M. Métivier;P. Priouret
考虑了两类一般的随机算法，包括Ljung考虑的算法以及\theta ＿n+1{ = }\theta ＿n{ - }\gamma ＿n+1 {V＿n+1}（{}\theta ＿n{， Z）的算法，其中Z是一个平稳遍历过程。它展示了如何应用库什纳和克拉克的引理来获得这些算法的性质。这是通过在广义Ljung情况下使用特定的鞅参数来实现的。在这些不同的情况下，在经典有界假设下，用相关常微分方程的方法得到了收敛性。对于线性算法，放弃了有界性假设。}
Two general classes of stochastic algorithms are considered, including algorithms considered by Ljung as well as algorithms of the form \theta_{n+1} = \theta_{n} - \gamma_{n+1} V_{n+1}(\theta_{n}, Z) , where Z is a stationary ergodic process. It is shown how one can apply a lemma of Kushner and Clark to obtain properties of these algorithms. This is done by using in particular Martingale arguments in the generalized Ljung case. In these various situations the convergence is obtained by the method of the associated ordinary differential equation, under the classical boundedness assumptions. In the case of linear algorithms, the boundedness assumptions are dropped.