值域更新问题

Range-renewal problems

本文是有关"值域更新"问题的综述.首先简要回顾了随机游动(及Brown运动)有关值域问题研究的历史脉络.本文给出独立同分布(i.i.d.)/连分数/简单对称随机游动三类模型下的"值域更新"结构定理,并提出一些公开问题与猜测.

In this paper, we give a simple survey on the so-called range-renewal problems. We first briefly review the history of related researches on random walks. Then we present range-renewal structure theorems for i.i.d./continued fractions/simple symmetrical random walks models and also some open problems and conjectures.