A Resummed Branching Process Representation for a Class of Nonlinear ODEs
Francesco Morandin, Università degli Studi di Parma, Italy
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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