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December 2019 Right marker speeds of solutions to the KPP equation with noise
Sandra Kliem
Ann. Appl. Probab. 29(6): 3637-3694 (December 2019). DOI: 10.1214/19-AAP1489

Abstract

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.

Citation

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Sandra Kliem. "Right marker speeds of solutions to the KPP equation with noise." Ann. Appl. Probab. 29 (6) 3637 - 3694, December 2019. https://doi.org/10.1214/19-AAP1489

Information

Received: 1 October 2018; Revised: 1 April 2019; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172343
MathSciNet: MR4047989
Digital Object Identifier: 10.1214/19-AAP1489

Subjects:
Primary: 60H15
Secondary: 35R60

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 6 • December 2019
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