Potential Analysis

, Volume 15, Issue 4, pp 361–408 | Cite as

A Support Theorem for a Generalized Burgers SPDE

  • Caroline Cardon-Weber
  • Annie Millet
Article

Abstract

When the initial condition u0 to a parabolic Burgers SPDE (containing a quadratic term) belongs to L q [0,1],2≤q≤∞, 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.

approximations support theorem Burgers' stochastic partial differential equation Brownian sheet 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Caroline Cardon-Weber
    • 1
  • Annie Millet
    • 1
  1. 1.Laboratoire de Probabilités UMR 7599Université Paris 6Paris cedex 05France

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