数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (3): 845-856.doi: 10.1007/s10473-019-0313-4

• 论文 • 上一篇    下一篇

UNIQUENESS PROBLEM FOR SPDES FROM POPULATION MODELS

熊捷1, 杨叙2   

  1. 1. Department of Mathematicss, Southern University of Science and Technology, Shenzhen 518055, China;
    2. School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
  • 收稿日期:2018-03-23 修回日期:2018-05-28 出版日期:2019-06-25 发布日期:2019-06-27
  • 通讯作者: Xu YANG E-mail:xuyang@mail.bnu.edu.cn
  • 作者简介:Jie XIONG,E-mail:xiongj@sustc.edu.cn
  • 基金资助:
    Supported partially by SUST startup fund 28/Y01286120, NSF of Ningxia (2018AAC03245), NSFC (11771018), and First-Class Disciplines Foundation Ningxia (NXYLXK2017B09).

UNIQUENESS PROBLEM FOR SPDES FROM POPULATION MODELS

Jie XIONG1, Xu YANG2   

  1. 1. Department of Mathematicss, Southern University of Science and Technology, Shenzhen 518055, China;
    2. School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
  • Received:2018-03-23 Revised:2018-05-28 Online:2019-06-25 Published:2019-06-27
  • Contact: Xu YANG E-mail:xuyang@mail.bnu.edu.cn
  • Supported by:
    Supported partially by SUST startup fund 28/Y01286120, NSF of Ningxia (2018AAC03245), NSFC (11771018), and First-Class Disciplines Foundation Ningxia (NXYLXK2017B09).

摘要: This is a survey on the strong uniqueness of the solutions to stochastic partial differential equations (SPDEs) related to two measure-valued processes:superprocess and Fleming-Viot process which are given as rescaling limits of population biology models. We summarize recent results for Konno-Shiga-Reimers' and Mytnik's SPDEs, and their related distribution-function-valued SPDEs.

关键词: Stochastic partial differential equation, superprocess, Fleming-Viot process, distribution function, backward doubly stochastic differential equation, pathwise uniqueness

Abstract: This is a survey on the strong uniqueness of the solutions to stochastic partial differential equations (SPDEs) related to two measure-valued processes:superprocess and Fleming-Viot process which are given as rescaling limits of population biology models. We summarize recent results for Konno-Shiga-Reimers' and Mytnik's SPDEs, and their related distribution-function-valued SPDEs.

Key words: Stochastic partial differential equation, superprocess, Fleming-Viot process, distribution function, backward doubly stochastic differential equation, pathwise uniqueness

中图分类号: 

  • 60H15