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Asymptotic properties of the solutions to stochastic KPP equations

Published online by Cambridge University Press:  11 July 2007

B. Øksendal ,
G. Våge  and
H. Z. Zhao
B. Øksendal
Affiliation:
Department of Mathematics, University of Oslo, Box 1053 Blindern, N-0316 Oslo, Norway and Norwegian School of Economics and Business Administration, Helleveien 30, N-5035 Bergen-Sandviken, Norway
G. Våge
Affiliation:
Department of Mathematics, University of Oslo, Box 1053 Blindern, N-0316 Oslo, Norway
H. Z. Zhao
Affiliation:
Department of Mathematics, University of California, Irvine, CA 92697, USA and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK
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Abstract

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A reduction method is used to prove the existence and uniqueness of strong solutions to stochastic Kolmogorov–Petrovskii–Piskunov (KPP) equations, where the initial condition may be anticipating. The asymptotic behaviour of the solution for large time and space and the random travelling waves are then studied under two different basic assumptions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 6 , December 2000 , pp. 1363 - 1381
Copyright
Copyright © Royal Society of Edinburgh 2000