On mean-field super-Brownian motions
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On mean-field super-Brownian motions. / Hu, Yaozhong; Kouritzin, Michael A.; Xia, Panqiu; Zheng, Jiayu.
In: Annals of Applied Probability, Vol. 33, No. 5, 2023, p. 3872-3915.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - On mean-field super-Brownian motions
AU - Hu, Yaozhong
AU - Kouritzin, Michael A.
AU - Xia, Panqiu
AU - Zheng, Jiayu
N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2023.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - branching particle systems
KW - mean-field stochastic partial differential equation
KW - moment conditions
KW - moment differentiability
KW - moment formula
KW - Super-Brownian motion
U2 - 10.1214/22-AAP1909
DO - 10.1214/22-AAP1909
M3 - Journal article
AN - SCOPUS:85176807075
VL - 33
SP - 3872
EP - 3915
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 5
ER -
ID: 382452514