University of SaskatchewanHARVEST
  • Login
  • Submit Your Work
  • About
    • About HARVEST
    • Guidelines
    • Browse
      • All of HARVEST
      • Communities & Collections
      • By Issue Date
      • Authors
      • Titles
      • Subjects
      • This Collection
      • By Issue Date
      • Authors
      • Titles
      • Subjects
    • My Account
      • Login
      JavaScript is disabled for your browser. Some features of this site may not work without it.
      View Item 
      • HARVEST
      • Electronic Theses and Dissertations
      • Graduate Theses and Dissertations
      • View Item
      • HARVEST
      • Electronic Theses and Dissertations
      • Graduate Theses and Dissertations
      • View Item

      Law of large numbers for monotone convolution

      Thumbnail
      View/Open
      WENDLER-THESIS.pdf (407.5Kb)
      Date
      2014-09-19
      Author
      Wendler, Enzo
      Type
      Thesis
      Degree Level
      Masters
      Metadata
      Show full item record
      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.
      Degree
      Master of Science (M.Sc.)
      Department
      Mathematics and Statistics
      Program
      Mathematics
      Supervisor
      Wang, Jiun-Chau
      Committee
      Srinivasan, Raj; Samei, Ebrahim; Dutchyn, Christopher
      Copyright Date
      September 2014
      URI
      http://hdl.handle.net/10388/ETD-2014-09-1693
      Subject
      Law of large numbers
      monotone convolution
      Non-commutative probability theory
      Markov chains and martingales
      Collections
      • Graduate Theses and Dissertations
      University of Saskatchewan

      University Library

      The University of Saskatchewan's main campus is situated on Treaty 6 Territory and the Homeland of the Métis.

      © University of Saskatchewan
      Contact Us | Disclaimer | Privacy