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

doi:10.1007/s10473-023-0612-7

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2519-2532.doi: 10.1007/s10473-023-0612-7

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

Ruinan LI¹, Xinyu WANG^2,†

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

收稿日期:2022-05-25 修回日期:2023-06-07 发布日期:2023-12-08
通讯作者: †Xinyu Wang, E-mail: wang_xin_yu2000@hotmail.com
作者简介:Ruinan LI, E-mail: ruinanli@amss.ac.cn
基金资助:
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).

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

Ruinan LI¹, Xinyu WANG^2,†

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

Received:2022-05-25 Revised:2023-06-07 Published:2023-12-08
Contact: †Xinyu Wang, E-mail: wang_xin_yu2000@hotmail.com
About author:Ruinan LI, E-mail: ruinanli@amss.ac.cn
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).

摘要/Abstract

摘要： 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.

关键词: stochastic heat equation, transportation cost-information inequality, fractional-colored noise

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.

Key words: stochastic heat equation, transportation cost-information inequality, fractional-colored noise

中图分类号:

60H15

Ruinan LI, Xinyu WANG. TRANSPORTATION COST-INFORMATION INEQUALITY FOR A STOCHASTIC HEAT EQUATION DRIVEN BY FRACTIONAL-COLORED NOISE^*[J]. 数学物理学报(英文版), 2023, 43(6): 2519-2532.

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.

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

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

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