Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### A support theorem for a generalized Burgers SPDE

Auteur(s):

Code(s) de Classification MSC:

Résumé: When the initial condition $u_0$ to a parabolic Burgers SPDE (containing a quadratic term) belongs to $L^q[0,1]$, $2 \leq q \leq \infty$ , the trajectories of the solution $u(t,x)$ a.s. belong to the space $C([0,T],L^q[0,1])$. We characterize the support of the law of $u$ in this space; the proof is based on an approximation of $u$ by a sequence of stochastic processes obtained by replacing the Brownian sheet by linear adapted interpolations