Erratum to Branching-coalescing particle systems (Probab. Theory Relat. Fields, (2005), 131, 376-414, DOI: 10.1007/s00440-004-0377-4);Branching-coalescing particle systems

Probability Theory and Related Fields

Volumn 131, Issue 3, 2005, Pages 376-414

  Arthreya, Siva R ^a   Swart, Jan M ^b  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Autocatalytic reaction; Branching; Coalescence; Contact process; First Schl gl Model; Mutation; Reaction diffusion process; Resampling; Selection

Indexed keywords

EID: 18244377150     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-009-0232-8     Document Type: Erratum

References (25)

1. [BEM03] Blath, J., Etheridge, A.M., Meredith, M.E.: Coexistence in locally regulated competing populations. University of Oxford, Preprint, 2003
2. [BES02] Barton, N.H., Etheridge, A.M., Sturm, A.K.: Coalescence in a random background. WIAS Berlin, Preprint No. 756, 2002. To appear in Ann. Appl. Probab.
3. [Che87] Chen, M.F.: Existence theorems for interacting particle systems with non-compact state space. Sci. China Ser. A 30, 148-156 (1987)
4. [Daw93] Dawson, D.A.: Measure-valued Markov processes. In: PL. Hennequin (ed.), École d'été de probabilités de Saint Flour XXI-1991, volume 1541 of Lecture Notes in Mathematics, Springer, Berlin, 1993, pp. 1-260
5. [DG99] 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), 81 (1999)
6. [DDL90] Ding, W., Durrett, R., Liggett, T.M.: Ergodicity of reversible reaction diffusion processes. Probab. Theory Relat. Fields 85 (1), 13-26 (1990)
7. [DK99] Donelly, P., Kurtz, T.G.: Genealogical processes for Fleming-Viot models with selection and recombination. Ann. Appl. Probab. 9, 1091-1148 (1999)
8. [EK86] Ethier, S.N., Kurtz, T.G.: Markov Processes; Characterization and Convergence. John Wiley & Sons, New York, 1986
9. [FS03a] Fleischmann, K., Swart, J.M. Extinction versus exponential growth in a supercritical super-Wright-Fisher diffusion. Stochastic Processes Appl. 106 (1), 141-165 (2003)
10. [FS03b] Fleischmann, K., Swart, J.M. Trimmed trees and embedded particle systems. WIAS Berlin, Preprint No. 793, 2002. To appear in Ann. Probab.
11. [Ka183] Kallenberg, O.: Random measures. 3rd rev. and enl. ed. Akademie-Verlag, Berlin, 1983
12. [KN97] Krone, S.M., Neuhauser, C.: Ancestral processes with selection. Theor. Popul. Biol. 51 (3), 210-237 (1997)
13. [Lig85] Liggett, T.M.: Interacting Particle Systems. Springer-Verlag, New York, 1985
14. [Lig99] Liggett, T.M. Stochastic Interacting Systems: Contact, Voter and Exclusion Process. Springer-Verlag, Berlin, 1999
15. [LS81] Liggett, T.M., Spitzer, F.: Ergodic theorems for coupled random walks and other systems with locally interacting components. Z. Wahrsch. verw. Gebiete 56, 443-468 (1981)
16. [Mou92] Mountford, T.S.: The ergodicity of a class of reversible reaction-diffusion processes. Probab. Theory Relat. Fields 92 (2), 259-274 (1992)
17. [MT95] Müller, C., Tribe, R.: Stochastic p.d.e.'s arising from the long range contact and long range voter processes. Probab. Theory Relat. Fields 102 (4), 519-545 (1995)
18. [Neu90] Neuhauser, C.: An ergodic theorem for Schlögl models with small migration. Probab. Theory Relat. Fields 85 (1), 27-32 (1990)
19. [Sch72] Schlögl, F.: Chemical reaction models and non-equilibrium phase transitions. Z. Phys. 253, 147-161 (1972)
20. [Shi81] Shiga, T.: Diffusion processes in population genetics. J. Math. Kyoto Univ. 21, 133-151 (1981)
21. [SS80] Shiga, T., Shimizu, A.: Infinite dimensional stochastic differential equations and their applications. J. Math. Kyoto Univ. 20, 395-416 (1980)
22. [SU86] Shiga, T., Uchiyama, K.: Stationary states and their stability of the stepping stone model involving mutation and selection. Probab. Theory Relat. Fields 73, 87-117 (1986)
23. [Swa99] Swart, J.M.: Large Space-Time Scale Behavior of Linearly Interacting Diffusions. PhD thesis, Katholieke Universiteit Nijmegen, 1999 http://helikon.ubn.kun.nl/mono/s/swart_j/largspscb.pdf.
24. [Swa00] Swart, J.M.: Clustering of linearly interacting diffusions and universality of their long-time limit distribution. Probab. Theory Relat. Fields 118, 574-594 (2000)
25. [YW71] Yamada, T., Watanabe, S.: On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11, 155-167 (1971)