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A Resummed Branching Process Representation for a Class of Nonlinear ODEs


 
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1. Title Title of document A Resummed Branching Process Representation for a Class of Nonlinear ODEs
 
2. Creator Author's name, affiliation, country Francesco Morandin; Università degli Studi di Parma, Italy
 
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4. Description 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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7. Date (YYYY-MM-DD) 2005-02-24
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1126
 
10. Identifier Digital Object Identifier 10.1214/ECP.v10-1126
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 10
 
12. Language English=en
 
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