This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed, we assume that they follow a regime-switching Markov chain. For this model, we (1) give finite sample bounds on the expected occupancy probabilities, and (2) provide detailed asymptotics in the case where the underlying distribution is regularly varying. We find that in the regularly varying case the finite sample bounds are rate optimal and have, up to a constant, the same rate of decay as the asymptotic result.

中文翻译：

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关于制度切换模型的占用问题

本文研究了字母表上的预期占用概率。与假设观察值是独立且同分布的标准情况不同，我们假设它们遵循状态切换马尔可夫链。对于这个模型，我们 (1) 给出了预期占用概率的有限样本界限，并且 (2) 在底层分布规律变化的情况下提供了详细的渐近线。我们发现，在规则变化的情况下，有限样本边界是速率最优的，并且在恒定范围内具有与渐近结果相同的衰减速率。