On the Attracting Orbit of a Non-Linear Transformation Arising From Renormalization Of Hierarchically Interacting Diffusions Part I: The Compact Case
Canadian journal of mathematics, Tome 47 (1995) no. 1, pp. 3-27

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This paper analyzes the n-fold composition of a certain non-linear integral operator acting on a class of functions on [0,1 ]. The attracting orbit is identified and various properties of convergence to this orbit are derived. The results imply that the space-time scaling limit of a certain infinite system of interacting diffusions has universal behavior independent of model parameters.
DOI : 10.4153/CJM-1995-001-2
Mots-clés : 60K35, 47H99
Baillon, J. B.; Clément, PH.; Greven, A.; Hollander, F. Den. On the Attracting Orbit of a Non-Linear Transformation Arising From Renormalization Of Hierarchically Interacting Diffusions Part I: The Compact Case. Canadian journal of mathematics, Tome 47 (1995) no. 1, pp. 3-27. doi: 10.4153/CJM-1995-001-2
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Breiman, L., Probability, Addison-Wesley, Reading, 1968. Google Scholar

Cox, J. T. and Greven, A., On the long term behavior of finite particle systems: a critical dimension example. In: Random Walks, Brownian Motion and Interacting Particle Systems, A Festschrift in Honor of Frank Spitzer, (eds. Durrett, R. and Kesten, H.), Progr. Probab. 28, Birkhauser, Boston, 1991. 203–213. Google Scholar

Cox, J.T., Greven, A. and Shiga, T., Finite and infinite systems of interacting diffusions, Probab. Theory Related Fields, to appear. Google Scholar

Dawson, D.A. and Greven, A., Multiple time scale analysis of hierarchically interacting systems. Stochastic Processes, A Festschrift in Honour of Gopinath Kallianpur, (eds. Cambanis, S., Ghosh, J.K., Karandikar, R.L. and Sen, P.K.), Springer, New York, 1993. 41–50. Google Scholar

Dawson, D.A. , Hierarchical models of interacting diffusions: multiple time scale phenomena, phase transition and pattern of cluster-formation, Probab. Theory Related Fields 96(1993), 435–473. Google Scholar

Dawson, D.A., Greven, A. and Vaillancourt, J., Equilibria and quasi-equilibria for infinite collections of interacting Fleming-Viotprocesses, Trans. Amer. Math. Soc, to appear. Google Scholar

Durrett, R., Lecture Notes on Particle Systems and Percolation, Wadsworth Brooks-Cole, Pacific Grove, 1988. Google Scholar

Fleischmann, K. and Greven, A., Diffusive clustering in an infinite system of hierarchically interacting diffusions, IAAS Berlin, 1992., Probab. Theory Related Fields 98(1994), 517–566. Google Scholar

Georgii, H.-O., Gibbs Measures and Phase Transitions, Walter de Gruyter, Berlin, 1988. Google Scholar

Liggett, T., Interacting Particle Systems, Springer, New York, 1985. Google Scholar

Ohta, T. and Kimura, M., A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population, Genet. Res. Camb. 22(1973), 201–204. Google Scholar

[] Shiga, T., An interacting system in population genetics, J. Math. Kyoto Univ. 20(1980), I: 213-243, II: 723-733. Google Scholar

[] Sawyer, S. and Felsenstein, J., Isolation by distance in a hierarchically clustered population, J. Appl. Probab. 20(1983), 1–10. Google Scholar

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