论文标题
一些简单随机步行及其最大过程
Some Martingale Properties of Simple Random Walk and Its Maximum Process
论文作者
论文摘要
在本文中，研究了与简单的随机步行有关的群众及其最大过程。首先，有一个充分的条件，在该条件下，具有三个参数，时间，随机步行及其最大过程的函数将呈现一个曲目，并且作为应用程序，提供了一种推导肯尼迪·马丁格（Kennedy Martingale）的替代方法。然后，提出了具有两个参数的函数的完整表征，即随机步行及其最大值，即the派。这个马丁加尔可以被视为Azéma-Yor Martingale的离散版本。由于Yor Martingale的离散Azéma的应用，提供了DOOB不平等的证据，并提供了离散的Azéma-YOR解决方案是Skorokhod嵌入问题的简单随机步行问题的解决方案，并详细介绍了简单的随机步行。
In this paper, martingales related to simple random walks and their maximum process are investigated. First, a sufficient condition under which a function with three arguments, time, the random walk, and its maximum process becomes a martingale is presented, and as an application, an alternative way of deriving the Kennedy martingale is provided. Then, a complete characterization of a function with two arguments, the random walk and its maximum, being a martingale is presented. This martingale can be regarded as a discrete version of the Azéma--Yor martingale. As applications of discrete Azéma--Yor martingale, a proof of the Doob's inequalities is provided and a discrete Azéma--Yor solution for the Skorokhod embedding problem for the simple random walk is formulated and examined in detail.
