Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On a conjecture of Révész

Author: Qi Man Shao
Journal: Proc. Amer. Math. Soc. 123 (1995), 575-582
MSC: Primary 60F15; Secondary 60G17
MathSciNet review: 1231304
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \{ {X_n},n \geq 1\} $ be i.i.d. random variables with $ P({X_i} = \pm 1) = \frac{1}{2}$. Révész (1990) proved

\begin{displaymath}\begin{array}{*{20}{c}} {1 \le \mathop {\lim \inf }\limits_{n... ...- {S_j}) \le K\quad {\rm {a}}.{\rm {s}}.} \hfill \\ \end{array}\end{displaymath}

and conjectured $ K = 1$, where $ {S_n} = \sum\nolimits_{i = 1}^n {{X_i}} $. In this we show that Révész's conjecture is true but the conclusion is not valid for general i.i.d. random variables with finite moment generating function.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60F15, 60G17

Retrieve articles in all journals with MSC: 60F15, 60G17

Additional Information

PII: S 0002-9939(1995)1231304-9
Keywords: Increments, partial sums, a.s. convergence, random walk
Article copyright: © Copyright 1995 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia