A distribution-function-valued SPDE and its applications

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• 作者：Li Wang^a ; ^{wangli@mail.buct.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xu Yang^b ; ^{xuyang@mail.bnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xiaowen Zhou^c ; ^{xiaowen.zhou@concordia.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60H15 ; 60F15 ; 60J80
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：262
• 期：2
• 页码：1085-1118
• 全文大小：416 K

文摘

In this paper we further study the stochastic partial differential equation first proposed by Xiong [22]. Under localized conditions on its coefficients, we prove a comparison theorem on its solutions and show that the solution is in fact distribution-function-valued. We also establish pathwise uniqueness of the solution. As applications we obtain the well-posedness of martingale problems for two classes of measure-valued diffusions: interacting super-Brownian motions and interacting Fleming–Viot processes. Properties of the two superprocesses such as the existence of density fields and the survival–extinction behaviors are also studied.