Resumen de Taylor expansion of the density in a stochastic heat equation

Marta Sanz Solé, David Márquez Carreras

• We prove a general result on asymptotic expansions of densities for families of perturbed Wiener functionals. As an application, we consider a stochastic heat equation driven by a space-time white noise $\varepsilon \dot{W}_{t,x}, \varepsilon\in (0, 1]$. The main theorem describes the asymptotics, as $\varepsilon\downarrow 0$, of the density $p^\varepsilon_{t,x}(y)$ of the solution at a fixed point ($t, x$) for some particular value $y\in\mathbb{R}$, which, in the diffusion case, plays the role of the diagonal.