Doctoral Dissertations

Keywords and Phrases

Grüss inequality; Ostrowski inequality

Abstract

"In this dissertation, the recently discovered concept of time scales is applied to probability theory, thus unifying discrete, continuous and many other cases. A short introduction to the theory of time scales is provided. Following this preliminary overview, the moment generating function is derived using a Laplace transformation on time scales. Various unifications of statements and new theorems in statistics are shown. Next, distributions on time scales are defined and their properties are studied. Most of the derived formulas and statements correspond exactly to those from discrete and continuous calculus and extend the applicability to many other cases. Some theorems differ from the ones found in the literature, but improve and simplify their handling. Finally, applications to finance, economics and inequalities of Ostrowski and Grüss type are presented. Throughout this paper, our results are compared to their well known counterparts in discrete and continuous analysis and many examples are given"--Abstract, page iii.

Advisor(s)

Bohner, Martin, 1966-

Committee Member(s)

Akin, Elvan
Gelles, Gregory M.
Wen, Xuerong
Morgan, Ilene H.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Fall 2011

Pagination

viii, 174 pages

Note about bibliography

Includes bibliographical references (pages 169-173).

Rights

© 2011 Thomas Matthews, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Subject Headings

Differentiable dynamical systemsFree probability theory

Thesis Number

T 9901

Print OCLC #

794763561

Electronic OCLC #

763228012

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Included in

Mathematics Commons

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