论文标题
随机收缩映射定理
A Stochastic Contraction Mapping Theorem
论文作者
论文摘要
在本文中，我们为适应的随机过程定义了合同和非专业属性$ x_1，x_2，\ ldots $，可用于推断限制属性。通常，非专业过程具有有限的限制，而承包过程则融合到零$ a.e. $扩展到多变量流程。这些属性可用于建模许多重要过程，包括对受控线性模型的随机近似和最小二乘估计，并具有从单个理论中得出的收敛性能。该方法的优点通常不需要分析规则性属性，例如连续性和可不同。
In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive processes converge to zero $a.e.$ Extensions to multivariate processes are given. These properties may be used to model a number of important processes, including stochastic approximation and least-squares estimation of controlled linear models, with convergence properties derivable from a single theory. The approach has the advantage of not in general requiring analytical regularity properties such as continuity and differentiability.
