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Research Article | Open Access

Existence and uniqueness of solutions for stochastic differential equations with locally one-sided Lipschitz condition

Fangfang Shen, Huaqin Peng( )
School of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi, 541004, China
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Abstract

This paper investigated stochastic differential equations (SDEs) with locally one-sided Lipschitz coefficients. Apart from the local one-sided Lipschitz condition, a more general condition was introduced to replace the monotone condition. Then, in terms of Euler's polygonal line method, the existence and uniqueness of solutions for SDEs was established. In the meanwhile, the pth moment boundedness of solutions was also provided.

Keywords

stochastic differential equationslocally one-sided Lipschitzexistence and uniquenessmoment boundedness
CLC number: 60H10, 34F99

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 22578-22589
DOI: 10.3934/math.20241099

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Cite this article:
Shen F, Peng H. Existence and uniqueness of solutions for stochastic differential equations with locally one-sided Lipschitz condition. AIMS Mathematics, 2024, 9(8): 22578-22589. https://doi.org/10.3934/math.20241099

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Received: 25 April 2024
Revised: 27 June 2024
Accepted: 10 July 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)