Re-equilibration on Higher Level E1 (Phase 4)
Chapter
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Abstract
Having now handled phases 0,1,2,3, in this section we are concerned with Phase 4 (recall Subsubsection 4.2.1 for the five phases scenario), that is, the time regime in which the mean-field model on spatial level 2 is concentrated on the second fitness level (E 1 types) and approaches a McKean–Vlasov mutation-selection equilibrium but before the emergence of the third fitness level (E 2-types) in a typical spatial 1-ball. This will then also serve as Phase 0 for the transition E 1 → E 2 in a model at spatial scale 2 which will be considered in the next section.
Keywords
Fitness Level Path Space Martingale Problem Exponential Moment Uniform Topology
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References
- [DG99]D.A. Dawson, A. Greven, Hierarchically interacting Fleming-Viot processes with selection and mutation: Multiple space time scale analysis and quasi equilibria. Electron. J. Probab. 4, paper no. 4, 1–81 (1999)Google Scholar
- [DGV]D.A. Dawson, A. Greven, J. Vaillancourt, Equilibria and Quasi-equilibria for Infinite Collections of Interacting Fleming-Viot processes. Trans. Am. Math. Soc. 347(7), 2277–2360 (1995)MathSciNetMATHGoogle Scholar
- [JN]P. Jagers, O. Nerman, The growth and composition of branching populations. Adv. Appl. Probab. 16, 221–259 (1984)MathSciNetCrossRefMATHGoogle Scholar
- [LO]R.M. Loynes, Extreme values in uniformly mixing stationary stochastic processes. Ann. Math. Stat. 36, 993–999 (1965)MathSciNetCrossRefMATHGoogle Scholar
- [MZ]P.A. Meyer, W.A. Zheng, Tightness criteria for laws of semimartingales. Ann. l’Institut Henri Poincaré 20, 353–372 (1984)MathSciNetMATHGoogle Scholar
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