Stochastic stability, time-dependent mutations, and empirical distribution.

Cheung, Man Wah.Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.Includes bibliographical references (leaves 50-53).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Stochastic Stability --- p.2Chapter 1.2 --- Some Examples --- p.3Chapter 1.3 --- Our Main Focus --- p.5Chapter 1.4 --- Thesis Outline --- p.6Chapter 2 --- KMR's Approach and its Variations --- p.7Chapter 2.1 --- KMR's Approach --- p.7Chapter 2.2 --- Variations --- p.12Chapter 2.2.1 --- Bergin and Lipman (1996) --- p.12Chapter 2.2.2 --- Anderlini and Ianni (1996) --- p.12Chapter 2.2.3 --- Robson and Vega-Redondo (1996) --- p.13Chapter 2.2.4 --- Robles (1998) and Pak (2008) --- p.13Chapter 3 --- Mathematical Reviews on Nonstationary Markov Chain --- p.15Chapter 3.1 --- Ergodic Coefficient --- p.15Chapter 3.2 --- Weak Ergodicity --- p.16Chapter 3.3 --- Strong Ergodicity --- p.18Chapter 4 --- Existing Works on Time-Dependent Mutation Rates --- p.20Chapter 4.1 --- Model and Definitions --- p.20Chapter 4.2 --- Sufficient Condition for Weak Ergodicity --- p.23Chapter 4.3 --- Sufficient Condition for Strong Ergodicity --- p.24Chapter 5 --- Time-Dependent Mutations and Empirical Distribution --- p.26Chapter 5.1 --- Model --- p.28Chapter 5.2 --- Convergence of Empirical Distribution --- p.30Chapter 5.3 --- Proofs of Claims --- p.35Chapter 5.3.1 --- Proofs of Claims l(a)-(d) --- p.36Chapter 5.3.2 --- Proof of Claim 2 --- p.39Chapter 6 --- Open Problems --- p.42Chapter 6.1 --- Numerical Example and Simulations --- p.43Chapter 6.2 --- Numerical Results --- p.44Chapter 6.3 --- Other Discussions --- p.47Chapter 7 --- Conclusion --- p.48Bibliography --- p.5