随机变量正部的特征函数及相关结果与应用
概率论
2017-01-17 v3
摘要
设 为任意实值随机变量（r.v.），其特征函数（c.f.）为 。本文给出了随机变量 的特征函数关于 的积分表达式，以及其他相关结果。展示了其在股票期权和随机游走中的应用。特别是，获得了 Spitzer 恒等式的一种更明确且紧凑的形式。
引用
@article{arxiv.1309.5928,
title = {Characteristic function of the positive part of a random variable and related results, with applications},
author = {Iosif Pinelis},
journal= {arXiv preprint arXiv:1309.5928},
year = {2017}
}
备注
2 pages. Version 2: 3 pages; a formula for the c.f. of |X| and three references are added; discussion expanded; title and abstract changed; Version 3: 9 pages; the paper is completely reworked; title and abstract changed; applications are given; in particular, a more explicit and compact form of Spitzer's identity is presented