Applications of Extreme Point Methods to Probability Theory
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Bowling Green State University / OhioLINK
1975
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| Online Access: | http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1566297715170558 |
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ndltd-OhioLink-oai-etd.ohiolink.edu-bgsu15662977151705582021-08-03T07:12:35Z Applications of Extreme Point Methods to Probability Theory O'Connor, Thomas A. Mathematics In 1966, S. Johansen made use of Choquets' Theorem, a result in Functional Analysis, to obtain the Levy-Khinchine canonical form of infinitely divisible characteristic functions. This representation was first discovered in the 1930’s and has numerous applications in Probability Theory. Johansen's work was very gratifying in the sense that it displayed much interplay between the disciplines of Functional Analysis and Probability. The purpose of this thesis is to continue exploration of extreme point methods and their applications to Probability Theory. The major part of this dissertation concerns itself with extending Johansen's work to include n-dimensional infinitely divisible characteristic functions. If one is to follow the ingenious methods of Johansen, one has to know solutions of various functional equations in this more general setting. These projects occupy the first portion of the dissertation. In the final section of this paper, we derive Khinchine's representation of unimodal distributions through the use of extreme points. 1975 English text Bowling Green State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1566297715170558 http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1566297715170558 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |
| collection |
NDLTD |
| language |
English |
| sources |
NDLTD |
| topic |
Mathematics |
| spellingShingle |
Mathematics O'Connor, Thomas A. Applications of Extreme Point Methods to Probability Theory |
| author |
O'Connor, Thomas A. |
| author_facet |
O'Connor, Thomas A. |
| author_sort |
O'Connor, Thomas A. |
| title |
Applications of Extreme Point Methods to Probability Theory |
| title_short |
Applications of Extreme Point Methods to Probability Theory |
| title_full |
Applications of Extreme Point Methods to Probability Theory |
| title_fullStr |
Applications of Extreme Point Methods to Probability Theory |
| title_full_unstemmed |
Applications of Extreme Point Methods to Probability Theory |
| title_sort |
applications of extreme point methods to probability theory |
| publisher |
Bowling Green State University / OhioLINK |
| publishDate |
1975 |
| url |
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1566297715170558 |
| work_keys_str_mv |
AT oconnorthomasa applicationsofextremepointmethodstoprobabilitytheory |
| _version_ |
1719456067690168320 |