We study some probabilistic representations, based on branching processes, of a simple non-linear differential equation, i.e. u’=λu(auR − 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. © 2005 Applied Probability Trust.
A Resummed branching process representation for a class of nonlinear odes
Morandin F.
2005-01-01
Abstract
We study some probabilistic representations, based on branching processes, of a simple non-linear differential equation, i.e. u’=λu(auR − 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. © 2005 Applied Probability Trust.File in questo prodotto:
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