The law of the iterated logarithm for tail sums

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dc.contributor.author Ghimire, Santosh
dc.date.accessioned 2012-04-25T18:59:40Z
dc.date.available 2012-04-25T18:59:40Z
dc.date.issued 2012-04-25
dc.identifier.uri http://hdl.handle.net/2097/13647
dc.description.abstract The main purpose of this thesis is to derive the law of the iterated logarithm for tail sums in various contexts in analysis. The various contexts are sums of Rademacher functions, general dyadic martingales, independent random variables and lacunary trigonometric series. We name the law of the iterated logarithm for tail sums as tail law of the iterated logarithm. We first establish the tail law of the iterated logarithm for sums of Rademacher functions and obtain both upper and lower bound in it. Sum of Rademacher functions is a nicely behaved dyadic martingale. With the ideas from the Rademacher case, we then establish the tail law of the iterated logarithm for general dyadic martingales. We obtain both upper and lower bound in the case of martingales. A lower bound is obtained for the law of the iterated logarithm for tail sums of bounded symmetric independent random variables. Lacunary trigonometric series exhibit many of the properties of partial sums of independent random variables. So we finally obtain a lower bound for the tail law of the iterated logarithm for lacunary trigonometric series introduced by Salem and Zygmund. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Law of the iterated logarithm en_US
dc.subject dyadic martingales en_US
dc.subject Lacunary series en_US
dc.subject Rademacher functions en_US
dc.subject tail law of the iterated logarithm en_US
dc.title The law of the iterated logarithm for tail sums en_US
dc.type Dissertation en_US
dc.description.degree Doctor of Philosophy en_US
dc.description.level Doctoral en_US
dc.description.department Department of Mathematics en_US
dc.description.advisor Charles N. Moore en_US
dc.subject.umi Mathematics (0405) en_US
dc.date.published 2012 en_US
dc.date.graduationmonth May en_US


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