Permanental sequences with non-symmetric kernels that are generalization of the potentials of a Markov chain with state space $\{0,1/2, \ldots, 1/n,\ldots\}$ that was introduced by Kolmogorov, are studied. Depending on a parameter in the kernels we obtain an exact rate of divergence of the sequence at $0$, an exact local modulus of continuity of the sequence at $0$, or a precise bounded discontinuity for the sequence at $0$.

中文翻译：

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与 Kolmogorov 的马尔可夫链示例相关的永久序列

研究了具有非对称核的永久序列，该序列是 Kolmogorov 引入的状态空间为 $\{0,1/2, \ldots, 1/n,\ldots\}$ 的马尔可夫链势的推广。根据内核中的参数，我们在 $0$ 处获得序列的精确发散率，在 $0$ 处获得序列连续性的精确局部模数，或在 $0$ 处获得序列的精确有界不连续性。