A support theorem for a generalized Burgers SPDE (Q5952187)

Parabolic Burgers stochastic partial differential equations are considered. For the initial condition in \( L^q [0,1]\), \(2\leq q< \infty\), trajectories of the solution \(u(x,t)\) belong to \(C([0,T], L^q [0,1])\). The paper gives a characterization of the support of the law of \(u\) in this space. This extends the theorem of \textit{D. W. Stroock} and \textit{S. R. S. Varadhan} [in: Proc. 6th Berkeley Symp. Math. Stat. Probab., Univ. Calif. 1970, 3, 333-359 (1972; Zbl 0255.60056)].