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

  • Weak Convergence
  • Tightness
  • Base
  • Probability Measures
  • Compactification
  • Replication

• Graduation date

  Fall 2017

• 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.