Errors Theory using Dirichlet Forms, Linear Partial Differential Equations and Wavelets
Abstract
We present an application of error theory using Dirichlet Forms in linear partial differential equations (LPDE). We study the transmission of an uncertainty on the terminal condition to the solution of the LPDE thanks to the decomposition of the solution on a wavelets basis. We analyze the basic properties and a particular class of LPDE where the wavelets bases show their powerful, the combination of error theory and wavelets basis justifies some hypotheses, helpful to simplify the computation.
 Publication:

arXiv eprints
 Pub Date:
 August 2007
 arXiv:
 arXiv:0708.1073
 Bibcode:
 2007arXiv0708.1073S
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Probability;
 35K15 (Primary);
 60J45;
 65C20 (Secondary)
 EPrint:
 17 pages, some misprints corrected