In this paper, we prove Talagrand's $ T_2 $ 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 $H\in\left(\frac12,\,1\right)$, and is correlated for the spatial variable. The Girsanov theorem for fractional-colored Gaussian noise plays an important role in the proof.
Ruinan LI
,
Xinyu WANG
. TRANSPORTATION COST-INFORMATION INEQUALITY FOR A STOCHASTIC HEAT EQUATION DRIVEN BY FRACTIONAL-COLORED NOISE*[J]. Acta mathematica scientia, Series B, 2023
, 43(6)
: 2519
-2532
.
DOI: 10.1007/s10473-023-0612-7
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