Multiscale Analysis: Fisher-Wright Diffusions with Rare Mutations and Selection, Logistic Branching System

Springer Proceedings in Mathematics

Volumn 11, Issue , 2012, Pages 373-408

  Dawson, Donald A ^a   Greven, Andreas ^b  

^a CARLETON UNIVERSITY   (Canada)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

RANDOM PROCESSES;

BRANCHING RANDOM WALKS; BRANCHING SYSTEMS; FISHER-WRIGHT MODEL; LOCAL POPULATIONS; MULTI SCALE ANALYSIS; PARTICLE POPULATION; SCARCE RESOURCES; SPATIAL INTENSITY;

DIFFUSION;

EID: 84904136852     PISSN: 21905614     EISSN: 21905622     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-642-23811-6_15     Document Type: Article

References (26)

1. Bürger, R.: The Mathematical Theory of Selection, Recombination, and Mutation, Wiley (2001)
2. Cox, J.T., Dawson, D.A., Greven, A.:Mutually catalytic super branching random walks: Large finite systems and renormalization analysis. Memoirs of the AMS, 171, No. 809, 2nd of 4 numbers (2004)
3. Dawson, D.A.: Measure-valued Markov Processes. In: École d' Été de Probabilités de Saint Flour XXI, Lecture Notes in Mathematics, 1541, pp. 1-261. Springer (1993)
4. Dawson, D.A., Greven, A.: Multiple time scale analysis of interacting diffusions. Probab. Theory Rel. Fields, 95, 467-508 (1993)
5. Dawson, D.A., Greven, A.: Hierarchical models of interacting diffusions: multiple time scale phenomena. Phase transition and pattern of cluster-formation. Probab. Theory Rel. Fields, 96, 435-473 (1993)
6. Dawson, D.A., Greven, A.: Multiple space-time scale analysis for interacting branching models. Electron. J. Probab. 1(14), 1-8 (1996)
7. Dawson, D.A., Greven, A.: Hierarchically interacting Fleming-Viot processes with selection and mutation: Multiple space time scale analysis and quasi equilibria. Electron. J. Probab. 4(4), 1-81 (1999)
8. Dawson, D., Greven, A.: On the effects of migration in spatial Fleming-Viot models with selection and mutation, in preparation (2011)
9. Dawson, D.A., Greven, A., Vaillancourt, J.: Equilibria and Quasi-equilibria for infinite systems of Fleming-Viot processes. Trans. Am. Math. Soc. 347(7), 2277-2360 (1995)
10. Dawson, D.A., Kurtz, T.G.: Applications of duality to measure-valued diffusions. Springer Lecture Notes in Control and Inf. Sci. 42, 177-191 (1982)
11. Dawson, D.A., Greven, A.: Invasion by rare mutants in a spatial two-type system with selection, arXiv:1104.0253v1[math.PR] (2011)
12. Dawson, D.A., Greven, A.: Duality for spatially interacting Fleming-Viot processes with mutation and selection, arXiv:1104.1099v1[math.PR] (2011)
13. Depperschmidt, A., Greven, A., Pfaffelhuber, P.: Tree-valued Fleming-Viot dynamics with mutation and selection, Submitted to Annals of Probab. (2010)
14. Ethier, S.N., Kurtz, T.: Markov Processes. Characterization and Convergence, Paperback reprint in 2005, Wiley, New York (1986)
15. Ethier, S.N., Kurtz, T.G.: Convergence to Fleming-Viot processes in the weak atomic topology. Stoch. Process Appl. 54, 1-27 (1994)
16. Gärtner, J.: On theMcKean-Vlasov limit for interacting diffusions. Math. Nachr. 137, 197-248 (1988)
17. Greven, A., Pfaffelhuber, P., Winter, A.: Convergence in distribution of random metric measure spaces (The Λ-coalescent measure tree). PTRF 145(1), 285-322 (2009)
18. Greven, A., Pfaffelhuber, P., Winter, A.: Tree-valued resampling dynamics: Martingale problems and applications, submitted to PTRF 2010.
19. Hutzenthaler, M.: The virgin island model. Electr. J. Probab. 14, 1117-1161 (2009)
20. Jagers, P.: Stability and instability in population dynamics. J. Appl. Probab. 29, 770-780 (1992)
21. Jagers, P., Nerman, O.: The growth and composition of branching populations. Adv. in Appl. Probab. 16, 221-259 (1984)
22. McKean, H.P. Jr.: A class of Markov processes associated with nonlinear parabolic equations. Proc. N.A.S., USA 56, 1907-19 (1966)
23. Nerman, O.: On the convergence of supercritical general (C-M-J) branching processes. Zeitschrift f. Wahrscheinlichkeitsth. verw. Gebiete 57, 365-395 (1981)
24. Pitman, J., Yor, M.: A decomposition of Bessel bridges. Z. Wahr. verw. Geb. 59, 425-457 (1982)
25. Rogers, L.C.G., Williams, D.: Diffusions, Markov processes and martingales. 2, Wiley (1987)
26. Schirmeier, F.: A spatial population model in separating time windows. Master thesis, Department Mathematik, Erlangen (2010)