Travelling wave solutions to the KPP equation with branching noise arising from initial conditions with compact support

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• 作者：Sandra Kliem ^{sandra.kliem@uni-due.de}
• 关键词：primary ; 60H15 ; secondary ; 35R60
• 刊名：Stochastic Processes and their Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：127
• 期：2
• 页码：385-418
• 全文大小：446 K
• 卷排序：127

文摘

We consider the one-dimensional KPP-equation driven by space–time white noise and extend the construction of travelling wave solutions arising from initial data f0(x)=1∧(−x∨0)f0(x)=1∧(−x∨0) from (Tribe, 1996) to f0f0 non-negative continuous functions with compact support. As an application the existence of travelling wave solutions is used to prove that the support of any solution to the SPDE is recurrent. As a by-product, several upper measures are introduced that allow for a stochastic domination of any solution to the SPDE at a fixed point in time.