Transportation inequalities for stochastic heat equation with rough dependence in space
It is shown that with weighted \({L^2}\)-norm the Talagrand's transportation inequality \({{\mathbf{T}}_2}\) [\textit{M. Talagrand}, Geom. Funct. Anal. 6, No. 3, 587--600 (1996; Zbl 0859.46030)] holds for the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter \(1/4 < H < 1/2\) in the space variable.
scientific article; zbMATH DE number 7625347
scientific article