Limiting behaviors of generalized elephant random walks
Limiting behaviors of generalized elephant random walks
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DOI：
10.1063/5.0105789
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发表时间：
2022-06
影响因子：
1.3
通讯作者：
Yuichi Shiozawa
中科院分区：
文献类型：
--
作者：
Yuichi Shiozawa
研究了整数格上广义大象随机游动的极限行为。这种随机行走是通过使用两个参数序列来定义的，这些参数序列分别表示来自整个过去的每一步的记忆和每一步向右的漂移。该模型也被认为是一个相依的伯努利过程。我们的结果揭示了标度因子是如何由参数的行为决定的。特别地，我们允许参数的简并性。我们还给出了几个显式计算标度因子的例子。
We study the limiting behaviors of a generalized elephant random walk on the integer lattice. This random walk is defined by using two sequences of parameters expressing the memory at each step from the whole past and the drift of each step to the right, respectively. This model is also regarded as a dependent Bernoulli process. Our results reveal how the scaling factors are determined by the behaviors of the parameters. In particular, we allow the degeneracy of the parameters. We further present several examples in which the scaling factors are explicitly computed.