An algebraic approach to Pólya processes
Pouyanne, Nicolas
Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, p. 293-323 / Harvested from Project Euclid
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Pólya processes are natural generalizations of Pólya–Eggenberger urn models. This article presents a new approach of their asymptotic behaviour via moments, based on the spectral decomposition of a suitable finite difference transition operator on polynomial functions. Especially, it provides new results for large processes (a Pólya process is called small when 1 is a simple eigenvalue of its replacement matrix and when any other eigenvalue has a real part ≤1/2; otherwise, it is called large).
Publié le : 2008-04-15
Classification:  Pólya processes,  Pólya–Eggenberger urn processes,  Strong asymptotics,  Finite difference transition operator,  Vector-valued martingale methods,  60F15,  60F17,  60F25,  60G05,  60G42,  60J05,  68W40 
@article{1207948221,
     author = {Pouyanne, Nicolas},
     title = {An algebraic approach to P\'olya processes},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {44},
     number = {2},
     year = {2008},
     pages = { 293-323},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1207948221}
}

Pouyanne, Nicolas. An algebraic approach to Pólya processes. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp.  293-323. http://gdmltest.u-ga.fr/item/1207948221/