Revistes Catalanes amb Accés Obert (RACO)

Density estimates on a parabolic SPDE

David Márquez-Carreras, M. Mellouk

Resum


We consider a general class of parabolic spde's
$$
\frac{\partial u^\varepsilon_{t,x}}{\partial t}=\frac{\partial^2 u^\varepsilon_{t,x}} {\partial x^2}+\frac{\partial}{\partial x} g(u^\varepsilon_{t,x})+f(u^\varepsilon_{t,x})+\varepsilon\sigma(u^\varepsilon_{t,x}) \dot W_{t,x},
$$
with $(t,x)\in [0,T]\times [0,1]$ and $\varepsilon \dot W_{t,x}$, $\varepsilon > 0$, a perturbed Gaussian space-time white noise. For $(t,x)\in (0,T]\times(0,1)$ we prove the called Davies and Varadhan-Léandre estimates of the density $p^\varepsilon_{t,x}$ of the solution $u^\varepsilon_{t,x}$.

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