University of Illinois at Urbana-Champaign
A Weak Type Inequality for Martingale Transforms and Other Subordinate Martingales
Abstract
dc:descriptionWe 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Suh, Jiyeon
- Contributors dc:contributor
-
- Burkholder, Donald L.
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3086191
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86815