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Stochastic differential equations with jump reflection at time-dependent barriers

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  • Slominski, Leszek
  • Wojciechowski, Tomasz

Abstract

We study existence, uniqueness and approximation of solutions of stochastic differential equations with jump reflection at time-dependent barriers. The basic idea in proofs consists in applying new existence and stability theorems on deterministic one-dimensional Skorokhod problem. Our results are new even in the classical case of one reflecting barrier.

Suggested Citation

  • Slominski, Leszek & Wojciechowski, Tomasz, 2010. "Stochastic differential equations with jump reflection at time-dependent barriers," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1701-1721, August.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:9:p:1701-1721
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    References listed on IDEAS

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    1. Burdzy, Krzysztof & Kang, Weining & Ramanan, Kavita, 2009. "The Skorokhod problem in a time-dependent interval," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 428-452, February.
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    Cited by:

    1. Falkowski, Adrian & Słomiński, Leszek, 2022. "SDEs with two reflecting barriers driven by semimartingales and processes with bounded p-variation," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 164-186.
    2. Falkowski, Adrian & Słomiński, Leszek, 2020. "Backward stochastic differential equations with two barriers and generalized reflection," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4746-4765.
    3. Hilbert, Astrid & Jarni, Imane & Ouknine, Youssef, 2020. "On reflected stochastic differential equations driven by regulated semimartingales," Statistics & Probability Letters, Elsevier, vol. 167(C).
    4. Thomas Kruse & Philipp Strack, 2019. "An Inverse Optimal Stopping Problem for Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 423-439, May.
    5. Falkowski, Adrian & Słomiński, Leszek, 2021. "Mean reflected stochastic differential equations with two constraints," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 172-196.
    6. Falkowski, Adrian & Słomiński, Leszek, 2017. "SDEs with constraints driven by semimartingales and processes with bounded p-variation," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3536-3557.
    7. Imane Jarni & Youssef Ouknine, 2021. "On Reflection with Two-Sided Jumps," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1811-1830, December.

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