论文标题
保守的随机步行
Conservative Random Walk
论文作者
论文摘要
最近，在[概率25（2020）的电子杂志“转变的步行及其缩放限制”中，在$ {\ Mathbb Z} $上引入了``转变的步行''。这是一个非马克维亚过程，其中的步骤形成了（可能）时间均匀的马尔可夫链。在本文中，我们通过在$ {\ mathbb z}^d $，$ d \ ge 2 $中引入类似过程来跟进调查：在时间$ n $上，该过程的方向为``更新''，概率$ p_n $;否则下一步重复上一步。我们研究这些步道的一些基本特性，例如瞬态/复发和缩放限制。 我们的结果补充了有关``相关''（或``newtonian''）和````'''''）和```''''''''''''''''的结果。
Recently, in ["The coin-turning walk and its scaling limit", Electronic Journal of Probability, 25 (2020)], the ``coin-turning walk'' was introduced on ${\mathbb Z}$. It is a non-Markovian process where the steps form a (possibly) time-inhomogeneous Markov chain. In this article, we follow up the investigation by introducing analogous processes in ${\mathbb Z}^d$, $d\ge 2$: at time $n$ the direction of the process is ``updated'' with probability $p_n$; otherwise the next step repeats the previous one. We study some of the fundamental properties of these walks, such as transience/recurrence and scaling limits. Our results complement previous ones in the literature about ``correlated'' (or ``Newtonian'') and ``persistent'' random walks.
