By now there is a solid theory for Polya urns. Finding the covariances is somewhat laborious. While these papers are “structural,” our purpose here is “computational.” We propose a practicable method for building the asymptotic covariance matrix in tenable balanced urn schemes, whereupon the asymptotic covariance matrix is obtained by solving a linear system of equations. We demonstrate the use of the method in growing tenable balanced irreducible schemes with a small index and in critical urns. In the critical case, the solution to the linear system of equations is explicit in terms of an eigenvector of the scheme.

中文翻译：

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Pólya urn 方案中的协方差

到目前为止，Polya 骨灰盒已经有了可靠的理论。寻找协方差有点费力。虽然这些论文是“结构性的”，但我们的目的是“计算性的”。我们提出了一种在可行的平衡缸方案中构建渐近协方差矩阵的实用方法，然后通过求解线性方程组获得渐近协方差矩阵。我们展示了该方法在具有小索引和关键骨灰盒中的可维持平衡不可约方案的使用。在临界情况下，线性方程组的解根据方案的特征向量是明确的。