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.
| Identifer | oai:union.ndltd.org:USASK/oai:ecommons.usask.ca:10388/ETD-2014-09-1693 |
| Date | 2014 September 1900 |
| Contributors | Wang, Jiun-Chau |
| Source Sets | University of Saskatchewan Library |
| Language | English |
| Detected Language | English |
| Type | text, thesis |
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