| Título: | Renormalization analysis of catalytic Wright-Fisher diffusions |
| Autores: |
Swart, Jan M.; UTIA Fleischmann, Klaus; WIAS Berlin |
| Fecha: | 2006-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Renormalization, catalytic Wright-Fisher diffusion, embedded particle system, extinction, unbounded growth, interacting diffusions, universality. 82C28;82C22;60J60;60J80 |
| Descripción: | Recently, several authors have studied maps where a function, describing the local diffusion matrix of a diffusion process with a linear drift towards an attraction point, is mapped into the average of that function with respect to the unique invariant measure of the diffusion process, as a function of the attraction point. Such mappings arise in the analysis of infinite systems of diffusions indexed by the hierarchical group, with a linear attractive interaction between the components. In this context, the mappings are called renormalization transformations. We consider such maps for catalytic Wright-Fisher diffusions. These are diffusions on the unit square where the first component (the catalyst) performs an autonomous Wright-Fisher diffusion, while the second component (the reactant) performs a Wright-Fisher diffusion with a rate depending on the first component through a catalyzing function. We determine the limit of rescaled iterates of renormalization transformations acting on the diffusion matrices of such catalytic Wright-Fisher diffusions. |
| Idioma: | No aplica |
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