Probability theory on time scales and applications to finance and inequalities

"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.

Name thesis:degree_name

Ph. D. in Mathematics

Grantor

Missouri University of Science and Technology

Year dc:date.available

2016

Author dc:creator

• Matthews, Thomas

• Grüss inequality
• Ostrowski inequality
• Mathematics

Repository record dc:identifier

https://scholarsmine.mst.edu/doctoral_dissertations/2241

OAI identifier oai:identifier

oai:scholarsmine.mst.edu:doctoral_dissertations-3243