Law of large numbers for monotone convolution

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Date
2014-09-19Author
Wendler, Enzo
Type
ThesisDegree Level
MastersMetadata
Show full item recordAbstract
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.
Degree
Master of Science (M.Sc.)Department
Mathematics and StatisticsProgram
MathematicsSupervisor
Wang, Jiun-ChauCommittee
Srinivasan, Raj; Samei, Ebrahim; Dutchyn, ChristopherCopyright Date
September 2014Subject
Law of large numbers
monotone convolution
Non-commutative probability theory
Markov chains and martingales