Longest interval between zeros of the tied-down random walk, the Brownian bridge and related renewal processes
Longest interval between zeros of the tied-down random walk, the Brownian bridge and related renewal processes
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束缚随机游走、布朗桥和相关更新过程的零点之间的最长间隔
DOI：
10.1088/1751-8121/aa6a6e
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
C. Godrèche
中科院分区：
文献类型：
--
作者：
C. Godrèche
Rosén 和 Wendel 过去分析了从原点开始和结束的简单随机游走的两个零之间的最长间隔及其连续极限（布朗桥）的概率分布，然后由后者扩展到稳定过程。我们使用更新理论的简单概念来恢复和扩展这些结果，这允许重新审视过去和最近的物理文献著作。
The probability distribution of the longest interval between two zeros of a simple random walk starting and ending at the origin, and of its continuum limit, the Brownian bridge, was analysed in the past by Rosén and Wendel, then extended by the latter to stable processes. We recover and extend these results using simple concepts of renewal theory, which allows to revisit past and recent works of the physics literature.