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Renormalization analysis of catalytic Wright-Fisher diffusions | | K. Fleischmann
; J. M. Swart
; | | Date: |
15 Jun 2005 | | Subject: | Probability MSC-class: 82C28 (Primary) 82C22, 60J60 (Secondary) | math.PR | | Abstract: | 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. | | Source: | arXiv, math.PR/0506311 | | Services: | Forum | Review | PDF | Favorites | |
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