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University of Illinois at Urbana-Champaign
Pointwise Relations Between Ergodic Averages and Martingales
Abstract
dc:descriptionIt is known that the ergodic averages An 4 , in the context of the shift action on Z , satisfy pointwise inequalities of the form An4≤CE4 &vbm0;Fn+E4 &vbm0;Gn , where {Fn}n ≥ 1 and {Gn} n ≥ 1 are decreasing sequences of sigma-algebras on Z . In this thesis we extend this by examining situations when the ergodic averages can be pointwise dominated by one reversed martingale, situations when a reversed martingale can be pointwise dominated by ergodic averages, and when differentiation averages can be dominated by a martingale.
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
-
- Goubran, Nader
- Contributors dc:contributor
-
- Rosenblatt, Joseph
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3070310
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86799