Nearby variables with nearby conditional laws and a strong approximation theorem for Hilbert space valued martingales
Nearby variables with nearby conditional laws and a strong approximation theorem for Hilbert space valued martingales
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具有邻近条件定律的邻近变量和希尔伯特空间值鞅的强近似定理
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
W. Philipp
中科院分区：
文献类型：
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作者：
D. Monrad;W. Philipp
本文主要研究不允许独立随机向量和强逼近其部分和的随机向量序列。在第一部分中，我们证明了条件版本的Strassen-Dudley定理。我们应用这些在第二部分的文件，以获得强不变的原则，向量值鞅，当适当规范化，收敛于法律的混合高斯分布。
SummaryIn this paper we focus on sequences of random vectors which do not admit a strong approximation of their partial sums by sums of independent random vectors. In the first part we prove conditional versions of the Strassen-Dudley theorem. We apply these in the second part of the paper to obtain strong invariance principles for vector-valued martingales which, when properly normalized, converge in law to a mixture of Gaussian distributions.