Transportation inequalities for doubly perturbed stochastic differential equations with Markovian switching

Liping Xu; Zhi Li; Weiguo Liu; Jie Zhou; Liping Xu; Zhi Li; Weiguo Liu; Jie Zhou

doi:10.3934/math.2021173

AIMS Mathematics

2021, Volume 6, Issue 3: 2874-2885. doi: 10.3934/math.2021173

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Research article

Transportation inequalities for doubly perturbed stochastic differential equations with Markovian switching

1.
School of Information and Mathematics, Yangtze University, Jingzhou, Hubei, 434023, P. R. China
2.
School of Statistics and Mathematics, Guangdong University of Finance & Economics, Guangzhou, Guangdong, 510320, P. R. China
3.
College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, Guangdong, 518060, P. R. China

Received: 22 October 2020 Accepted: 16 December 2020 Published: 07 January 2021
MSC : 60H15, 60G15, 60H05

In this paper, we focus on a class of doubly perturbed stochastic differential equations with Markovian switching. Using the Girsanov transformation argument we establish the quadratic transportation inequalities for the law of the solution of those equations with Markovian switching under the $ d_2 $ metric and the uniform metric $ d_{\infty} $.
- transportation inequalities,
- doubly perturbed SDEs,
- Girsanov transformation,
- Markovian switching
Citation: Liping Xu, Zhi Li, Weiguo Liu, Jie Zhou. Transportation inequalities for doubly perturbed stochastic differential equations with Markovian switching[J]. AIMS Mathematics, 2021, 6(3): 2874-2885. doi: 10.3934/math.2021173

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Abstract

In this paper, we focus on a class of doubly perturbed stochastic differential equations with Markovian switching. Using the Girsanov transformation argument we establish the quadratic transportation inequalities for the law of the solution of those equations with Markovian switching under the $ d_2 $ metric and the uniform metric $ d_{\infty} $.

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