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On the strong solutions of one-dimensional stochastic differential equations with reflecting boundary

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  • Zhang, Tu-Sheng

Abstract

In this paper, we directly prove the existence and uniqueness of a strong solution of the stochastic differential equations with reflecting boundary under the assumption of non-degenerate diffusion coefficient and measurable drift. Moreover, a Wong-Zakai type approximation theorem is obtained for the equations.

Suggested Citation

  • Zhang, Tu-Sheng, 1994. "On the strong solutions of one-dimensional stochastic differential equations with reflecting boundary," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 135-147, March.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:1:p:135-147
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    Cited by:

    1. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.
    2. S. Ramasubramanian, 2000. "A Subsidy-Surplus Model and the Skorokhod Problem in an Orthant," Mathematics of Operations Research, INFORMS, vol. 25(3), pages 509-538, August.
    3. Słomiński, Leszek, 2015. "On reflected Stratonovich stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 759-779.
    4. Zhao, Zhenwen & Xi, Yuejuan, 2021. "The first passage time on the (reflected) Brownian motion with broken drift hitting a random boundary," Statistics & Probability Letters, Elsevier, vol. 171(C).
    5. Lijun Bo & Yongjin Wang & Xuewei Yang, 2010. "Some integral functionals of reflected SDEs and their applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 343-348.
    6. Masanori Hino & Kouhei Matsuura & Misaki Yonezawa, 2021. "Pathwise Uniqueness and Non-explosion Property of Skorohod SDEs with a Class of Non-Lipschitz Coefficients and Non-smooth Domains," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2166-2191, December.
    7. P. Marín-Rubio & J. Real, 2004. "Some Results on Stochastic Differential Equations with Reflecting Boundary Conditions," Journal of Theoretical Probability, Springer, vol. 17(3), pages 705-716, July.
    8. Semrau-Giłka, Alina, 2015. "On approximation of solutions of one-dimensional reflecting SDEs with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 315-321.
    9. Wen Yue & Tusheng Zhang, 2015. "Absolute Continuity of the Laws of Perturbed Diffusion Processes and Perturbed Reflected Diffusion Processes," Journal of Theoretical Probability, Springer, vol. 28(2), pages 587-618, June.
    10. Słomiński, Leszek, 2013. "Weak and strong approximations of reflected diffusions via penalization methods," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 752-763.
    11. Gassiat, Paul & Mądry, Łukasz, 2023. "Perturbations of singular fractional SDEs," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 137-172.
    12. Yang, Saisai & Zhang, Tusheng, 2023. "Strong solutions to reflecting stochastic differential equations with singular drift," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 126-155.
    13. Chihoon Lee & Amy R. Ward & Heng-Qing Ye, 2020. "Stationary distribution convergence of the offered waiting processes for $$GI/GI/1+GI$$GI/GI/1+GI queues in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 147-173, February.

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