## A Foundations of probability theory

- Joseph Mark, Thomas Grigoryan
- 2003

- Published 2002

(t, x) ∈ [0, T ]×[0, 1], ε > 0, with initial condition u0,x = ξ(x) and Dirichlet’s boundary conditions ut,0 = u ε t,1 = 0. The process {Ẇt,x, (t, x) ∈ [0, T ] × [0, 1]} is a space-time white noise on a complete probability space (Ω,F , P ); σ, f, g : R → R are smooth functions and ξ is some real-valued function defined on [0, 1]. If σ = f = 0 and g(r) = r/2, the above equation is called Burgers equation. It arises connection with the study of turbulent fluid motion and the literature attaches great importance to this fact (see, for instance, [4]). Recently, Burgers equation perturbed by space-time white

@inproceedings{Mellouk2002DensityEO,
title={Density Estimates on a Parabolic Spde},
author={M. Mellouk and D. M{\'a}rquez-Carreras},
year={2002}
}