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Title:A Weak Type Inequality for Martingale Transforms and Other Subordinate Martingales
Author(s):Suh, Jiyeon
Doctoral Committee Chair(s):Burkholder, Donald L.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:We study a problem of finding the best constant in a weak type inequality for martingale transforms extending the result of Burkholder (1966). First, we study the inequality for the discrete-time martingale case. We present examples of martingales that give good lower estimates of the best constant. We then find a biconcave function to prove that the supremum of these lower estimates is in fact the best constant. We use this biconcave function to prove a sharp weak type inequality for differentially subordinate martingales with the same best constant, and by approximation a similar inequality for stochastic integrals. We generalize these results to the continuous-time case and give an application to harmonic functions.
Issue Date:2003
Type:Text
Language:English
Description:43 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.
URI:http://hdl.handle.net/2142/86815
Other Identifier(s):(MiAaPQ)AAI3086191
Date Available in IDEALS:2015-09-28
Date Deposited:2003


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