Some properties of superprocesses under a stochastic flow
Lee, Kijung ; Mueller, Carl ; Xiong, Jie
Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009), p. 477-490 / Harvested from Numdam
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Nous montrons que, sous un flot stochastique en dimension un, un superprocess a une densité par rapport à la mesure de Lebesgue. Nous déduisons une équation différentielle stochastique satisfaite par la densité. Nous montrons ensuite la régularité de la solution en utilisant la theorie de Krylov pour les EDPS linéaires dans Lp.

For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov's Lp-theory for linear SPDE.

Publié le : 2009-01-01
DOI : https://doi.org/10.1214/08-AIHP171
Classification:  60G57,  60H15,  60J80 
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     author = {Lee, Kijung and Mueller, Carl and Xiong, Jie},
     title = {Some properties of superprocesses under a stochastic flow},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {45},
     year = {2009},
     pages = {477-490},
     doi = {10.1214/08-AIHP171},
     mrnumber = {2521410},
     zbl = {1171.60011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2009__45_2_477_0}
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Lee, Kijung; Mueller, Carl; Xiong, Jie. Some properties of superprocesses under a stochastic flow. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) pp. 477-490. doi : 10.1214/08-AIHP171. http://gdmltest.u-ga.fr/item/AIHPB_2009__45_2_477_0/

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