HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING*

doi:10.1007/s10473-023-0323-0

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1403-1414.doi: 10.1007/s10473-023-0323-0

HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING^*

Wenyi Pei^1,†, Litan Yan², Zhenlong Chen³

1. School of Statistics and Mathematics, Zhejiang Gongshang University, Zhejiang 310018, China; Collaborative Innovation Center of Statistical Data Engineering, Technology & Application,Zhejiang Gongshang University, Hangzhou 310018, China;;
2. Department of Statistics, Donghua University, Shanghai 201620, China;
3. School of Statistics and Mathematics, Zhejiang Gongshang University,Hangzhou 310018, China

收稿日期:2021-12-16 修回日期:2022-07-05 出版日期:2023-06-25 发布日期:2023-06-06
通讯作者: ^† Wenyi Pei, E-mail: peiwenyi@163.com
作者简介:Litan Yan, E-mail: litanyan@dhu.edu.cn;Zhenlong Chen, E-mail: zlchenv@163.com
基金资助:
The research of L. Yan was partially supported by the National Natural Science Foundation of China (11971101). The research of Z. Chen was supported by National Natural Science Foundation of China (11971432) and the Natural Science Foundation of Zhejiang Province (LY21G010003). This paper was supported by the Collaborative Innovation Center of Statistical Data Engineering Technology & Application, the Characteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University- Statistics) and the First Class Discipline of Zhejiang-A (Zhejiang Gongshang University-Statistics).

HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING^*

Wenyi Pei^1,†, Litan Yan², Zhenlong Chen³

1. School of Statistics and Mathematics, Zhejiang Gongshang University, Zhejiang 310018, China; Collaborative Innovation Center of Statistical Data Engineering, Technology & Application,Zhejiang Gongshang University, Hangzhou 310018, China;;
2. Department of Statistics, Donghua University, Shanghai 201620, China;
3. School of Statistics and Mathematics, Zhejiang Gongshang University,Hangzhou 310018, China

Received:2021-12-16 Revised:2022-07-05 Online:2023-06-25 Published:2023-06-06
Contact: ^† Wenyi Pei, E-mail: peiwenyi@163.com
About author:Litan Yan, E-mail: litanyan@dhu.edu.cn;Zhenlong Chen, E-mail: zlchenv@163.com
Supported by:
The research of L. Yan was partially supported by the National Natural Science Foundation of China (11971101). The research of Z. Chen was supported by National Natural Science Foundation of China (11971432) and the Natural Science Foundation of Zhejiang Province (LY21G010003). This paper was supported by the Collaborative Innovation Center of Statistical Data Engineering Technology & Application, the Characteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University- Statistics) and the First Class Discipline of Zhejiang-A (Zhejiang Gongshang University-Statistics).

摘要/Abstract

摘要： In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter $H$ is supposed to be in $(1/2,1)$. As a direct application, the strong Feller property is presented.

关键词: stochastic differential equations, Harnack type inequalities, fractional Brownian motion, Markovian switching

Abstract: In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter $H$ is supposed to be in $(1/2,1)$. As a direct application, the strong Feller property is presented.

Key words: stochastic differential equations, Harnack type inequalities, fractional Brownian motion, Markovian switching

Wenyi Pei, Litan Yan, Zhenlong Chen. HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING^*[J]. 数学物理学报(英文版), 2023, 43(3): 1403-1414.

Wenyi Pei, Litan Yan, Zhenlong Chen. HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1403-1414.

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HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING^*

HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING^*

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