From probability to PDEs : Stochastic differential equations and applications
The goal of this project is to give probabilistic representations of solution of different types of PDEs. In particular, we study the Brownian motion and relate this concept with the solution of linear PDEs. Moreover, we study the fractional Laplacian starting from long jump random walks. Finally, w...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2099.1/23138 |
| Acceso en línea: | https://hdl.handle.net/2099.1/23138 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations, Elliptic PDEs Brownian motion Brownian snake Random walks Equacions diferencials el·líptiques Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials |
| Sumario: | The goal of this project is to give probabilistic representations of solution of different types of PDEs. In particular, we study the Brownian motion and relate this concept with the solution of linear PDEs. Moreover, we study the fractional Laplacian starting from long jump random walks. Finally, we give a probabilistic solution of nonlinear PDEs thanks to the Brownian snake and relate this type of PDE with the singular Yamabe problem. |
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