RIGHT MARKER SPEEDS OF SOLUTIONS TO THE KPP EQUATION WITH NOISE

• 成果类型: Article
• 署名作者: Kliem, Sandra
• 署名单位: Goethe University Frankfurt
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1489
• 发表日期: 2019
• 页码: 3637-3694
• 关键词: contact

摘要

We consider the one-dimensional KPP-equation driven by space-time white noise. We show that for all parameters above the critical value for survival, there exist stochastic wavelike solutions which travel with a deterministic positive linear speed. We further give a sufficient condition on the initial condition of a solution to attain this speed. Our approach is in the spirit of corresponding results for the nearest-neighbor contact process respectively oriented percolation. Here, the main difficulty arises from the moderate size of the parameter and the long range interaction. Stopping times and averaging techniques are used to overcome this difficulty.