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Existence and uniqueness of solutions for perturbed stochastic differential equations with reflected boundary

  • Faiz Bahaj EMAIL logo and Kamal Hiderah ORCID logo
Published/Copyright: October 24, 2023

Abstract

In this paper, under some suitable conditions, we prove existence of a strong solution and uniqueness for the perturbed stochastic differential equations with reflected boundary (PSDERB), that is,

{ x ( t ) = x ( 0 ) + 0 t σ ( s , x ( s ) ) d B ( s ) + 0 t b ( s , x ( s ) ) d s + α ( t ) H ( max 0 u t x ( u ) ) + β ( t ) L t 0 ( x ) , x ( t ) 0 for all t 0 ,

where 𝐻 is a continuous R-valued function, σ , b , α and 𝛽 are measurable functions, L t 0 denotes a local time at point zero for the time of the semi-martingale 𝑥.

MSC 2010: 60H10; 60J60

Acknowledgements

We are thankful to the editor and the anonymous referee for very careful reading, and her/his valuable remarks and suggestions which led to the improvement of the article.

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Received: 2022-12-09
Revised: 2023-09-19
Accepted: 2023-09-20
Published Online: 2023-10-24
Published in Print: 2024-03-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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