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

• Other Authors: Cheung, Man Wah.
• Format: Others
• Language: English; Chinese
• Published: 2010
• Subjects: Equilibrium (Economics) > Mathematical models; Stochastic processes
• Online Access: http://library.cuhk.edu.hk/record=b5894384; http://repository.lib.cuhk.edu.hk/en/item/cuhk-327225

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