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A Generalization of Martingale Theory to Self-Averaging Processes

Wang, Bo
Format
Thesis/Dissertation; Online
Author
Wang, Bo
Advisor
Gromoll, Christian
Abstract
We introduce and study a generalization of martingales with the following self-averaging property: at each time, the conditional expectation of future random variables given the past, is a weighted average of all the random variables comprising the past. We assume only that more recent random variables are weighted no less than older random variables. We investigate conditions under which important properties satisfied by martingales, such as maximal inequalities and convergence, are present in an appropriate form.
Language
English
Published
University of Virginia, Department of Mathematics, PHD (Doctor of Philosophy), 2017
Published Date
2017-04-30
Degree
PHD (Doctor of Philosophy)
Collection
Libra ETD Repository
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