论文标题
$ \ mathbb {z} $上的振荡随机步行
The oscillating random walk on $\mathbb{Z}$
论文作者
论文摘要
本文与Kemperman的意义上有关$ \ Mathbb {Z} $振荡过程的复发属性的新方法。如果随机步行在$ \ mathbb {z}^ - $上上升并在$ \ mathbb {z}^+$上下降时，我们确定了连续交叉时间的嵌入式过程的不变度度量，然后证明了必要的和充分的条件。最后，我们利用此结果表明在某些h {Ö} lder型时刻假设下，一般的振荡过程是复发的。
The paper is concerned with a new approach for the recurrence property of the oscillating process on $\mathbb{Z}$ in Kemperman's sense. In the case when the random walk is ascending on $\mathbb{Z}^-$ and descending on $\mathbb{Z}^+$, we determine the invariant measure of the embedded process of successive crossing times and then prove a necessary and sufficient condition for recurrence. Finally, we make use of this result to show that the general oscillating process is recurrent under some H{ö}lder-typed moment assumptions.
