Perturbed uncertain differential equations and perturbed reflected canonical process

Yuanbin Ma; Zhi Li; Yuanbin Ma; Zhi Li

doi:10.3934/math.2021562

AIMS Mathematics

2021, Volume 6, Issue 9: 9647-9659. doi: 10.3934/math.2021562

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Research article

Perturbed uncertain differential equations and perturbed reflected canonical process

Yuanbin Ma ,
Zhi Li ^,

School of Information and Mathematics, Yangtze University, Jingzhou 434023, China

Received: 03 January 2021 Accepted: 03 June 2021 Published: 28 June 2021
MSC : 26A33, 60G15, 60H15

In this paper, we consider a class of perturbed uncertain differential equations, which is a type of differential equations driven by canonical process. By the reflection principle and a successive approximation method, we obtain the existence and uniqueness of the solution to the considered equations. As an application, we establish the existence and uniqueness of some perturbed reflected canonical process.
- perturbed uncertain differential equations,
- canonical process,
- reflected diffusions,
- existence and uniqueness
Citation: Yuanbin Ma, Zhi Li. Perturbed uncertain differential equations and perturbed reflected canonical process[J]. AIMS Mathematics, 2021, 6(9): 9647-9659. doi: 10.3934/math.2021562

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Abstract

In this paper, we consider a class of perturbed uncertain differential equations, which is a type of differential equations driven by canonical process. By the reflection principle and a successive approximation method, we obtain the existence and uniqueness of the solution to the considered equations. As an application, we establish the existence and uniqueness of some perturbed reflected canonical process.

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