Document Type
Article
Publication Date
2-2007
Keywords
Linear delay differential equations, Asymptotic behavior, Sums of independent random variables, Random walks
Abstract
Let t⩾0. Select numbers randomly from the interval [0,1] until the sum is greater than t . Let α(t) be the expected number of selections. We prove that α(t)=et for 0⩽t⩽1. Moreover, . This limit is a special case of our asymptotic results for solutions of the delay differential equation f′(t)=f(t)-f(t-1) for t>1. We also consider four other solutions of this equation that are related to the above selection process.
Publication Title
Expositiones Mathematicae
Volume
25
Issue
1
First Page
1
Last Page
20
DOI
http://dx.doi.org/10.1016/j.exmath.2006.01.004
Required Publisher's Statement
Copyright © Elsevier B.V
This is the authors' post print version of the paper, the published version can be found at the links below.
doi:10.1016/j.exmath.2006.01.004
http://www.sciencedirect.com/science/article/pii/S0723086906000053
Recommended Citation
Ćurgus, Branko and Jewett, Robert I., "An Unexpected Limit of Expected Values" (2007). Mathematics Faculty Publications. 70.
https://cedar.wwu.edu/math_facpubs/70
Subjects - Topical (LCSH)
Differential equations, Linear; Asymptotic distribution (Probability theory); Random walks (Mathematics); Random variables
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
