Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60H15 Stochastic partial differential equations, See also {35R60}
- 60H05 Stochastic integrals

**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

**Mots Clés:** *approximations ; support theorem ; Burgers' stochastic partial differential equation ; Brownian sheet*

**Date:** 1999-05-19

**Prépublication numéro:** *PMA-503*