标题： 多色广义弗里德曼的伽马近似模型 显示英文标题

标题： The Gaussian approximation for multi-color generalized Friedman's urn model

摘要： 弗里德曼的瓮模型是一个流行的瓮模型，被广泛应用于许多学科。特别是在临床试验中的治疗分配方案中被广泛使用。在本文中，我们证明对于具有非齐次生成矩阵的多色广义弗里德曼瓮模型，瓮组成过程和分配比例过程都可以几乎必然地被多维高斯过程近似。高斯过程是随机微分方程的解。这种高斯近似以及高斯过程的性质对于理解瓮过程的行为非常重要，并且对于统计推断也有用。作为应用，我们得到了多色广义弗里德曼瓮模型的渐近性质，包括渐近正态性和迭代对数定律，以及随机玩赢规则作为特例。 显示英文摘要

摘要： The Friedman's urn model is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we prove that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman's urn model with non-homogeneous generating matrices. The Gaussian process is a solution of a stochastic differential equation. This Gaussian approximation together with the properties of the Gaussian process is important for the understanding of the behavior of the urn process and is also useful for statistical inferences. As an application, we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman's urn model as well as the randomized-play-the-winner rule as a special case.