| Título: | A General Analytical Result for Non-linear SPDE's and Applications |
| Autores: |
Denis, Laurent; Université du Maine, France Stoica, L.; University of Bucharest, Romania |
| Fecha: | 2004-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: | No aplica |
| Descripción: | Using analytical methods, we prove existence uniqueness and estimates for s.p.d.e. of the type $$ du_t+Au_tdt+f ( t,u_t ) dt+R g(t, u_t ) dt=h(t,x,u_t) dB_t, $$ where $A$ is a linear non-negative self-adjoint (unbounded) operator, $f$ is a nonlinear function which depends on $u$ and its derivatives controlled by $\sqrt{A}u$, $Rg$ corresponds to a nonlinearity involving $u$ and its derivatives of the same order as $Au$ but of smaller magnitude, and the right term contains a noise involving a $d$-dimensional Brownian motion multiplied by a non-linear function. We give a neat condition concerning the magnitude of these nonlinear perturbations. We also mention a few examples and, in the case of a diffusion generator, we give a double stochastic interpretation. |
| Idioma: | No aplica |
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