On mean-field super-Brownian motions

Hu, Yaozhong, Kouritzin, Michael A., Xia, Panqiu and Zheng, Jiayu 2023. On mean-field super-Brownian motions. The Annals of Applied Probability 33 (5) , pp. 3872-3915. 10.1214/22-AAP1909

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Abstract

The mean-field stochastic partial differential equation (SPDE) corresponding to a mean-field super-Brownian motion (sBm) is obtained and studied. In this mean-field sBm, the branching-particle lifetime is allowed to depend upon the probability distribution of the sBm itself, producing an SPDE whose space-time white noise coefficient has, in addition to the typical sBm square root, an extra factor that is a function of the probability law of the density of the mean-field sBm. This novel mean-field SPDE is thus motivated by population models where things like overcrowding and isolation can affect growth. A two step approximation method is employed to show the existence for this SPDE under general conditions. Then, mild moment conditions are imposed to get uniqueness. Finally, smoothness of the SPDE solution is established under a further simplifying condition.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Institute of Mathematical Statistics
ISSN:	1050-5164
Last Modified:	08 Aug 2024 14:00
URI:	https://orca.cardiff.ac.uk/id/eprint/171085

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