TRANSPORTATION COST-INFORMATION INEQUALITY FOR A STOCHASTIC HEAT EQUATION DRIVEN BY FRACTIONAL-COLORED NOISE*

  • Ruinan LI ,
  • Xinyu WANG
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  • 1. School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China;
    2. Wenlan School of Business, Zhongnan University of Economics and Law, Wuhan 430073, China
Ruinan LI, E-mail: ruinanli@amss.ac.cn

Received date: 2022-05-25

  Revised date: 2023-06-07

  Online published: 2023-12-08

Supported by

Li's research was supported by the Shanghai Sailing Program (21YF1415300) and the Natural Science Foundation of China (12101392). Wang's research was supported by the Natural Science Foundation of China (11871382, 11771161).

Abstract

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.

Cite this article

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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