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2005 A Resummed Branching Process Representation for a Class of Nonlinear ODEs
Francesco Morandin
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Electron. Commun. Probab. 10: 1-6 (2005). DOI: 10.1214/ECP.v10-1126

Abstract

We study some probabilistic representations, based on branching processes, of a simple nonlinear differential equation, i.e. $u'=\lambda u(au^R-1)$. The first approach is basically the same used by Le Jan and Sznitman for 3-d Navier-Stokes equations, which need small initial data to work. In our much simpler setting we are able to make this precise, finding all the cases where their method fails to give the solution. The second approach is based on a resummed representation, which we can prove to give all the solutions of the problem, even those with large initial data.

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Francesco Morandin. "A Resummed Branching Process Representation for a Class of Nonlinear ODEs." Electron. Commun. Probab. 10 1 - 6, 2005. https://doi.org/10.1214/ECP.v10-1126

Information

Accepted: 24 February 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1060.60085
MathSciNet: MR2119148
Digital Object Identifier: 10.1214/ECP.v10-1126

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