分数有色噪声驱动的随机热方程的运输成本信息不等式

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2023-11-06 DOI:10.1007/s10473-023-0612-7

Ruinan Li, Xinyu Wang

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引用次数: 0

摘要

在本文中，我们证明了高斯噪声驱动的随机热方程定律的Talagrand的T2运输成本信息不等式，该不等式对于具有Hurst指数的时间变量是分数的，并且对于空间变量是相关的。分数阶有色高斯噪声的Girsanov定理在证明中起着重要作用。

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

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.

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.