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On stability and existence of solutions of SDEs with reflection at the boundary

Author

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  • Rozkosz, Andrzej
  • Slominski, Leszek

Abstract

We study stability with respect to perturbation of coefficients and existence of weak solutions of stochastic differential equations with reflecting boundary conditions. We assume that the domain is a convex subset of d or satisfies quite general conditions introduced by Lions and Sznitman. The coefficients are merely measurable functions and the diffusion coefficients may degenerate on some subsets of the domain.

Suggested Citation

  • Rozkosz, Andrzej & Slominski, Leszek, 1997. "On stability and existence of solutions of SDEs with reflection at the boundary," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 285-302, June.
    • Handle: RePEc:eee:spapps:v:68:y:1997:i:2:p:285-302
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    Cited by:

    1. Chorowski, Jakub & Trabs, Mathias, 2016. "Spectral estimation for diffusions with random sampling times," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 2976-3008.
    2. 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.
    3. Gassous, Anouar M. & Răşcanu, Aurel & Rotenstein, Eduard, 2012. "Stochastic variational inequalities with oblique subgradients," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2668-2700.
    4. 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.
    5. 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.

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