论文标题
关于广义大象随机步行的限制行为的评论
Remarks on the limiting behaviors of generalized elephant random walks
论文作者
论文摘要
我们研究了整数晶格上一般大象随机行走的限制行为。通过使用两个参数序列来定义此随机步行，从整个过去和每个步骤的漂移向右表达内存。该模型也被视为依赖的Bernoulli过程。我们的结果揭示了缩放因子如何由参数的行为确定。特别是，我们允许参数的退化。我们进一步提供了几个示例，其中明确计算了缩放因子。
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.
