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

Fangfang Shen; Huaqin Peng; Fangfang Shen; Huaqin Peng

doi:10.3934/math.20241099

AIMS Mathematics

2024, Volume 9, Issue 8: 22578-22589. doi: 10.3934/math.20241099

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Research article

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

Received: 25 April 2024 Revised: 27 June 2024 Accepted: 10 July 2024 Published: 22 July 2024
MSC : 60H10, 34F99

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 $ p $th moment boundedness of solutions was also provided.
- stochastic differential equations,
- locally one-sided Lipschitz,
- existence and uniqueness,
- moment boundedness
Citation: Fangfang Shen, Huaqin Peng. Existence and uniqueness of solutions for stochastic differential equations with locally one-sided Lipschitz condition[J]. AIMS Mathematics, 2024, 9(8): 22578-22589. doi: 10.3934/math.20241099

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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 $ p $th moment boundedness of solutions was also provided.

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