论文标题
有条件随机晶格的条件随机步行的结构性特性，并随机局部约束
Structural Properties of Conditioned Random Walks on Integer Lattices with Random Local Constraints
论文作者
论文摘要
我们考虑在当地时代随机界限的多维整数晶格上随机步行，其条件是它在死亡前撞到高水平。我们引入了具有再生结构的辅助“核心”过程，并在我们的分析中起关键作用。根据“核心”过程的相似分布，我们获得了许多随机步行分布的表示。基于此，我们通过让高水平趋于无穷大，证明了许多限制结果。特别是，我们将结果推广到Benjamini和Berestycki（2010）早期在论文中获得的简单对称的一维随机步行。
We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary "core" process that has a regenerative structure and plays a key role in our analysis. We obtain a number of representations for the distribution of the random walk in terms of the similar distribution of the "core" process. Based on that, we prove a number of limiting results by letting the high level to tend to infinity. In particular, we generalise results for a simple symmetric one-dimensional random walk obtained earlier in the paper by Benjamini and Berestycki (2010).
