Hypercontractivity of order statistics and increments of fractional Brownian motion /
Let Xn n > 1, be a sequence of positive random numbers, let Xn,1 > Xn,2 > ...> Xn,n be the decreasing rearrangement of X,,. We are going to find necessary and sufficient conditions for hypercontractivity of the order statistics Xn,k when k is a constant. Then we will turn our attention...
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| Format: | Thesis Book |
| Language: | English |
| Published: |
[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=736579711&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Let Xn n > 1, be a sequence of positive random numbers, let Xn,1 > Xn,2 > ...> Xn,n be the decreasing rearrangement of X,,. We are going to find necessary and sufficient conditions for hypercontractivity of the order statistics Xn,k when k is a constant. Then we will turn our attention to the large increments of fractional Brownian motion. We prove series tests of the upper-upper and upper-lower classes for the large increments of fractional Brownian motion. We will also consider vector-valued fractional Brownian motion, the upper-upper and upper-lower classes for the large increments are then completely characterized. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | vi, 96 leaves ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 94-95. |