Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (6): 2519-2532.doi: 10.1007/s10473-023-0612-7

Previous Articles     Next Articles

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

Ruinan LI1, Xinyu WANG2,†   

  1. 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).

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

CLC Number: 

  • 60H15
Trendmd