Transportation cost-information inequality for a stochastic heat equation driven by fractional-colored noise

Abstract

In this paper, we prove Talagrand’s T₂ transportation cost-information inequality for the law of stochastic heat equation driven by Gaussian noise, which is fractional for a time variable with the Hurst index \(H \in ({1 \over 2},1)\), and is correlated for the spatial variable. The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof.