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Replication and Its Application to Weak Convergence

  • Author / Creator
    Dong, Chi
  • Herein, a new methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Each replica object is a weak or strong modification of the original object, so many results are easily established for the replica objects and then transferred back to the original ones. Two problems are solved within to demonstrate the method: (1) Finite-dimensional convergence to possibly non-cadlag limits is established for processes living on general topological spaces. (2) New tightness and relative compactness criteria are given for the Skorokhod space of Tychonoff-space-valued cadlag mappings. The methods herein are also used in companion papers to establish the: (3) existence of, uniqueness of and convergence to martingale problem solutions, (4) classical FKK and DMZ filtering equations and stationary filters, (5) finite-dimensional convergence to stationary signal-filter pairs, (6) invariant measures of Markov processes, and (7) Ray-Knight theory, all in general settings.

  • Subjects / Keywords
  • Graduation date
    2017-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3K06XF1W
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Kouritzin, Michael A. (Department of Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Dai, Feng (Department of Mathematical and Statistical Sciences)
    • Kouritzin, Michael A. (Department of Mathematical and Statistical Sciences)
    • Xiong, Jie (Department of Mathematics, University of Macau)
    • Frei, Christoph (Department of Mathematical and Statistical Sciences)
    • Kuttler, Jochen (Department of Mathematical and Statistical Sciences)