AI 中文总结
研究在巴拿赫空间中，噪声序列为均值0的独立同分布序列或满足适当矩条件的独立随机变量序列时的随机逼近，无需空间几何约束，证明相关结论及条件。
AI 中文摘要
本文主旨是表明在所有巴拿赫空间中，当噪声序列是均值为0的独立同分布序列时，随机逼近成立，且不对空间几何施加任何条件。同样，在矩的适当条件下，当噪声是独立随机变量序列时也成立，此时需要要求噪声序列是紧的。
英文摘要
The thrust of this article is to show that on all Banach spaces, stochastic approximation holds when the noise sequence is an i.i.d. sequence with mean 0, without imposing any condition on the geometry of the space. Also, the same is true when the noise is a sequence of independent random variables under appropriate conditions on the moment. In this case, we need to require that the noise sequence is tight.
