Characteristic function of the positive part of a random variable and related results, with applications
Probability
2017-01-17 v3
Abstract
Let be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) . Integral expressions for the c.f.\ of the r.v.'s in terms of are given, as well as other related results. Applications to stock options and random walks are presented. In particular, a more explicit and compact form of Spitzer's identity is obtained.
Keywords
Cite
@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}
}
Comments
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