Law of large numbers for monotone convolution
Date
2014-09-19
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Journal ISSN
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ORCID
Type
Degree Level
Masters
Abstract
In this thesis, we use martingales to show that the dilation of a sequence of monotone convolutions $D_\frac{1}{b_n} (\mu_1 \triangleright \mu_2 \triangleright \cdots \triangleright \mu_n)$ is stable, where $\mu_j$ are probability distributions with the condition $\sum \limits_{n=1}^\infty \frac{1}{b_n} \text{var}(\mu_n) < \infty$. This proves a law of large numbers for monotonically independent random variables.
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Keywords
Law of large numbers, monotone convolution, Non-commutative probability theory, Markov chains and martingales
Citation
Degree
Master of Science (M.Sc.)
Department
Mathematics and Statistics
Program
Mathematics