Degenerate stochastic differential equations for catalytic branching networks
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 4, pp. 943-980.

On prouve l'unicité d'un problème de martingale correspondant à une EDS dégénerée, qui apparaît comme un modèle de réseaux avec branchement catalytique. Ce travail est une extension des résultats de Dawson et Perkins [Illinois J. Math. 50 (2006) 323-383] au cas de réseaux généraux. On obtient en particulier des estimées pour le semi-groupe des réseaux généraux, sous forme de normes de Hölder pondérées; et on établit l'équivalence de ces normes avec des normes de semi-groupe dans ce contexte général.

Uniqueness of the martingale problem corresponding to a degenerate SDE which models catalytic branching networks is proven. This work is an extension of the paper by Dawson and Perkins [Illinois J. Math. 50 (2006) 323-383] to arbitrary catalytic branching networks. As part of the proof estimates on the corresponding semigroup are found in terms of weighted Hölder norms for arbitrary networks, which are proven to be equivalent to the semigroup norm for this generalized setting.

DOI : 10.1214/08-AIHP186
Classification : 60J60, 60J80, 60J35
Mots-clés : stochastic differential equations, martingale problem, degenerate operators, catalytic branching networks, diffusions, semigroups, weighted Hölder norms, perturbations 
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Kliem, Sandra. Degenerate stochastic differential equations for catalytic branching networks. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 4, pp. 943-980. doi : 10.1214/08-AIHP186. http://www.numdam.org/articles/10.1214/08-AIHP186/

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