关于平均场超布朗运动

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2023-10-01 DOI:10.1214/22-aap1909

Yaozhong Hu, Michael A. Kouritzin, Panqiu Xia, Jiayu Zheng

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引用次数: 2

摘要

研究了平均场超布朗运动的平均场随机偏微分方程(SPDE)。在这种平均场sBm中，允许分支粒子寿命取决于sBm本身的概率分布，从而产生一个SPDE，其时空白噪声系数除了具有典型sBm的平方根外，还有一个额外的因子，该因子是平均场sBm密度的概率律的函数。因此，这种新颖的平均场SPDE是由人口模型驱动的，在人口模型中，过度拥挤和孤立等因素会影响增长。用两步逼近法证明了该SPDE在一般条件下的存在性。然后，施加温和矩条件以获得唯一性。最后，在进一步简化的条件下，建立了SPDE解的平滑性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On mean-field super-Brownian motions

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.

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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.