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SDEs with constraints driven by semimartingales and processes with bounded p-variation

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  • Falkowski, Adrian
  • Słomiński, Leszek

Abstract

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded p-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:11:p:3536-3557
    DOI: 10.1016/j.spa.2017.03.003
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    References listed on IDEAS

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    1. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2008. "A singular stochastic differential equation driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2075-2085, October.
    2. 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.
    3. Rozkosz, Andrzej, 2003. "On a decomposition of symmetric diffusions with reflecting boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 101-122, January.
    4. Kubilius, K., 2002. "The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 289-315, April.
    5. 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.
    6. Aida, Shigeki, 2015. "Reflected rough differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3570-3595.
    7. Mishura, Yuliya & Shalaiko, Taras & Shevchenko, Georgiy, 2015. "Convergence of solutions of mixed stochastic delay differential equations with applications," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 487-497.
    8. Søren Asmussen, 1992. "Queueing Simulation in Heavy Traffic," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 84-111, February.
    9. Slominski, Leszek & Ziemkiewicz, Bartosz, 2009. "On weak approximations of integrals with respect to fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 543-552, February.
    10. Kubilius, K., 2008. "On the convergence of stochastic integrals with respect to p-semimartingales," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2528-2535, October.
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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, 2021. "Mean reflected stochastic differential equations with two constraints," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 172-196.
    3. Allan, Andrew L. & Liu, Chong & Prömel, David J., 2021. "Càdlàg rough differential equations with reflecting barriers," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 79-104.

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