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Travelling-waves for the FKPP equation via probabilistic arguments

1999; Cambridge University Press; Volume: 129; Issue: 3 Linguagem: Inglês

10.1017/s030821050002148x

1473-7124

Simon C. Harris,

Stochastic processes and financial applications

We outline a completely probabilistic study of travelling-wave solutions of the FKPP reaction-diffusion equation that are monotone and connect 0 to 1. The necessary asymptotics of such travelling-waves are proved using martingale and Brownian motion techniques. Recalling the connection between the FKPP equation and branching Brownian motion through the work of McKean and Neveu, we show how the necessary asymptotics and results about branching Brownian motion combine to give the existence and uniqueness of travelling waves of all speeds greater than or equal to the critical speed.