On mean-field super-Brownian motions

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

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

Harvard

Hu, Y, Kouritzin, MA, Xia, P & Zheng, J 2023, 'On mean-field super-Brownian motions', Annals of Applied Probability, vol. 33, no. 5, pp. 3872-3915. https://doi.org/10.1214/22-AAP1909

APA

Hu, Y., Kouritzin, M. A., Xia, P., & Zheng, J. (2023). On mean-field super-Brownian motions. Annals of Applied Probability, 33(5), 3872-3915. https://doi.org/10.1214/22-AAP1909

Vancouver

Hu Y, Kouritzin MA, Xia P, Zheng J. On mean-field super-Brownian motions. Annals of Applied Probability. 2023;33(5):3872-3915. https://doi.org/10.1214/22-AAP1909

Author

Hu, Yaozhong ; Kouritzin, Michael A. ; Xia, Panqiu ; Zheng, Jiayu. / On mean-field super-Brownian motions. In: Annals of Applied Probability. 2023 ; Vol. 33, No. 5. pp. 3872-3915.

Bibtex

@article{41c2e2d2bd314d7da2311fe123908ed9,
title = "On mean-field super-Brownian motions",
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.",
keywords = "branching particle systems, mean-field stochastic partial differential equation, moment conditions, moment differentiability, moment formula, Super-Brownian motion",
author = "Yaozhong Hu and Kouritzin, {Michael A.} and Panqiu Xia and Jiayu Zheng",
note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2023.",
year = "2023",
doi = "10.1214/22-AAP1909",
language = "English",
volume = "33",
pages = "3872--3915",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "5",

}

RIS

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