We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak convergence to a two-dimensional Gaussian process. Its covariance function depends only on exponent of regular decrease of probabilities. We obtain parameter estimates that have a normal asymototics for its joint distribution together with forward and backward processes. We use these estimates to construct statistical tests for the homogeneity of the urn scheme on the number of thrown balls.

翻译：我们在一个无限的内脏系统中研究前向和后向过程的非空脉冲数量的联合受试性。 假设蛋蛋撞击阴道的概率满足定期下降的条件。 我们证明我们与二维高斯过程的趋同程度不强。 它的共变性功能只取决于概率定期下降的推力。 我们获得参数估计值, 该参数具有正常的非摩托性, 以便与前向和后向过程联合分布。 我们用这些估计值来构建对抛出球数的蛋白质组合的同质性进行统计测试。