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.
Mots clés : superprocess, random environment, snake representation, stochastic partial differential equation
@article{AIHPB_2009__45_2_477_0, 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}, pages = {477--490}, publisher = {Gauthier-Villars}, volume = {45}, number = {2}, year = {2009}, doi = {10.1214/08-AIHP171}, mrnumber = {2521410}, zbl = {1171.60011}, language = {en}, url = {http://www.numdam.org/articles/10.1214/08-AIHP171/} }
TY - JOUR AU - Lee, Kijung AU - Mueller, Carl AU - Xiong, Jie TI - Some properties of superprocesses under a stochastic flow JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2009 SP - 477 EP - 490 VL - 45 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/08-AIHP171/ DO - 10.1214/08-AIHP171 LA - en ID - AIHPB_2009__45_2_477_0 ER -
%0 Journal Article %A Lee, Kijung %A Mueller, Carl %A Xiong, Jie %T Some properties of superprocesses under a stochastic flow %J Annales de l'I.H.P. Probabilités et statistiques %D 2009 %P 477-490 %V 45 %N 2 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/08-AIHP171/ %R 10.1214/08-AIHP171 %G en %F AIHPB_2009__45_2_477_0
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) no. 2, pp. 477-490. doi : 10.1214/08-AIHP171. http://www.numdam.org/articles/10.1214/08-AIHP171/
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